Here is Personal experience of the different Render Engines I made in past month / years :

• Redshift

  • Cuda and beta for Nvidia Optix
    • Metal OSX coming 
  • no CPU
  • forward pathtracing
  • no Cryptomatte 
  • great houdini support
  • deep image only in beta 3.0
  • biased rendering
    • good for superfast animation rendering
    • super useful indoor rendering
    • complex shader setup’s
  • Redshift RT
    • faster lookdev / turntables
    • good for stylized graphics
  • brute force path tracing
    • good stills
  • no standalone software
  • slow interactive render feedback
  • slow hair / splines rendering (long pre-run)
  • missing alpha transparency
  • commando lines tools
  • great AOV support
  • own render viewport

• Octane

  • Vulkan, Metal
    • OSX support soon
  • no CPU
  • forward pathtracing
  • Opacity / Alpha Mapping
  • no-good houdini support
  • no Cryptomatte 
  • slow hair / splines rendering (long pre-run)
  • no deformation motionBlur
  • hair primitives
  • volume displacement
  • volume procedurals
  • Brigade realtime engine
  • fast interactive render feedback
  • Spectral rendering
    • easy to setup for physical correct rendering
    • harder setup for custom shading
    • good for caustic / refraction
    • limited AOV support
  • standartalone software
    • save extra DDC licences
  • own render viewport
  • OSL support

• Arnold

  • GPU in beta for Nvidia Optix
  • no standalone software
  • cutting-edge algorithms
  • light instancing
  • Cryptomatte 
  • render state
  • render primitives
  • great houdini support
  • fast render feedback
  • extreme fast spline rendering
  • great shading models for hair
  • best volume renderer in terms of quality
  • unbeaten forward pathtracer
  • most easy going render software 
  • production proven (indestructible)
  • extreme volumes rendering
  • volumes displacements
  • missing alpha transparency 
  • lightpath expression
  • top edge image quality 
    • extreme good and fast hair /spline  shading
    • Subsurface scattering
  • no custom render viewport
  • OSL support

• Renderman

  • GPU in beta for Nvidia Optix
  • great houdini support
  • render primitives
  • Cryptomatte 
  • render state
  • interactive displacement 
  • always on lastest cutting edge render technology
  • no standalone software
  • fast render feedback
  • extreme fast spline rendering
  • forward pathtracing
  • great shading models for hair
  • light instancing
  • lightpath expression
  • extreme flexible renderer
  • alpha transparency support
  • great procedural shader collections
  • biased rendering
    • good for superfast animation rendering
    • complex shader setup’s
  • top edge image quality 
    • extreme good and fast hair /spline  shading
    • Subsurface scattering
  • bidirectional pathtracing
    • super useful indoor rendering
  • pathtrace guiding / manifold walk
    • extreme good for caustics / refraction
  • production proven (indestructible)
  • free for non commercial 
  • version 22.6 already Hydra ready (Houdini 18)
  • own render viewport
    • custome viewer have meta data support, click on pixel in the image to selection object/shader in DDC application
  • OSL support

• VRay

  • limited GPU version for Nividia Optix
    • GPU openCL version outdated and slow
  • Vray RT
    • still far away from final look
  • brute force pathtracing
  • great AOV support
  • alpha transparency support
  • great houdini support
  • complicated to setup 
  • production proven
  • large procedural shader collection
  • great shading models for hair
  • light instancing
  • baised rendering
    • good for superfast animation rendering
    • super useful indoor rendering
    • complex shader setup’s
  • no standalone software
  • Cryptomatte 
  • own render viewport
  • OSL support

External Engines

• indigo

  • openCL GPU runs super fast on Nvidia and AMD
  • CPU support for complex shading tracing techniques 
  • Spectral rendering
    • easy to setup for physical correct rendering
    • harder setup for custom shading
  • bidriectional rendering
    • good for indoor scenes
  • metropolis light transport
    • extreme good for caustics / refraction
  • custome viewer have meta data support, click on pixel in the image to selection object/shader in DDC application
  • only good for stills production visuals

• Evvee (Blender2.8)

  • openGL (nvidia and AMD
  • realtime graphics 
  • support VDB volumes
  • comes with a great 3d application 
  • typical limits of game engine
  • shader 1:1 to cycles
  • great for lookdev and final render in cycles
  • free, open source 

• Cycles (blender2.8)

  • comes with a great 3d application
  • forward path tracing
  • CPU and GPU (Nvidia and AMD)
  • free, open source
  • color depth limitation‘s
  • extreme good denoiser option’s
  • many versions in development / ready for test
    • gaffer version
    • spectral rendering

• Keyshot

  • Forward pathtracer
  • fastest CPU renderer beside Corona
  • GPU is coming
  • extreme good for VR
  • so easy even your Mom can use it
  • great HDRI editor
  • great default setup 
  • only good for stills production visuals

Each render algorithms has different benefit in different Scene / Light Situations.  Some common Render engines using following Algorithms:

Here is list Pro and Con based on my own Experience :   

Pathtracer

Pro :

• easy to use
• best for exteriors
• great characters and outdoor renderings

Con :

• bad for caustic
• not so good for interiors with much indirect lighting and small light sources

BiDirectional Pathtracing

Pro :

• very good for interiors
• good and fast caustic 

Con :

• not so fast for outdoor rendering
• slow for reflected caustics

Spectral Rendering

Pro :

• super easy to use
• most correct physics 
• mediun rendering
• make use of physical correct modeling
• great out of box image quality

Con :

• slower rendering 
• more memory use 32 floats instead 3
• need physical correct materials
• hard to get aov etc..
• shader limitation

Metropolis Light Transport

Pro : 

• faster for reflected caustic
• excellent for caustic
• best for interiors (indirect lighting, small light sources)

Con :

• very slow for exteriors

Path Guiding

Pro :

• extreme good for interiors (indirect lighting, small light sources)
• much faster than PT for scenes with very difficult lighting (e.g. light coming through a small opening, lighting the scene indirectly)
• fast caustics

Con :

• not so fast for glossy materials
• more setup time (tweaking render settings)
• problems with detailed geometry

Biased Rendering

Pro :

• fastest rendering
• very useful for caustics + reflected caustics
• most flexible render setups
• great shader hacks

Con :

• hard to setup
• need knowledge if optimization algorithms
• hard deal with large dataset
• biased, artefacts, splotchy, low frequency noise
• can have large memory footprint

stochastic progressive photon mapping

• best for indoor
• small memory footprint
• handles all kinds of caustics robustly

This is a quick overview of current render Engines for Houdini and General in terms of MotionGraphics and VFX usage. 

There are different RenderEngines out there, each one is unique and uses different method to solve a problem. I am looking into Arnold, RenderMan, Vray, Octane and Redshift. For comparison reason I added Indigo Renderer engine.

There are different way to render a scene with benefits and shortcomings. lets start with most common one.

image by Glare Technology

Pathtracing (PT)

to be precise Backward Pathtracing.  In backward ray tracing, an eye ray is created at the eye; it passes through the viewplane and on into the world.  The first object the eye ray hits is the object that will be visible from that point of the viewplane.  After the ray tracer allows that light ray to bounce around, it figures out the exact coloring and shading of that point in the viewplane and displays it on the corresponding pixel on the computer monitor screen. that’s classical way, which all of the Render engines uses as standard.

Metropolis light transport (MLT)

This procedure has the advantage, relative to bidirectional path tracing, that once a path has been found from light to eye, the algorithm can then explore nearby paths; thus difficult-to-find light paths can be explored more thoroughly with the same number of simulated photons. Metropolis light transport is an unbiased method that, in some cases (but not always), converges to a solution of the rendering equation faster than other unbiased algorithms such as path tracing or bidirectional path tracing. MetroPolis is often used in Bidirectional mode (BDMLT).

image by Silverwing

Path Guiding

Mix between Path-tracing and MLT, unbiased technique for intelligent light-path construction in path-tracing algorithms. Indirect Guiding that improves indirect lighting by sampling from the better lit or more important areas of the scene. goal is to allow path-tracing algorithms to iteratively “learn” how to construct high-energy light paths.

link to latest Siggraph paper

BiDirectional Pathtracing ( BDPT )

Regular backward Pathtracing has hard time in indoor scene with small light source because it take lot’s rays and bounce to find a tiny light in a room, just to see if a object gets light by the light.

with Bidirectional, rays are fired from both the camera and light sources. They are then joined together to create many complete light paths.

Spectral rendering

image by Silverwing

Unlike most renderers which work with RGB colours, Spectral renderers uses spectral colour throughout, from the physically-based sky model to the reflective and refractive properties of materials. The material models are completely based on the laws of physics.
This makes it possible to render transparent materials like glass and water at the highest degree of realism.
Spectral renderer are pretty good in simulate different medium atmospheric effects like under water or earth air atmosphere.

Biased Rendering

hat Biased Render Engine actually means is pre-computing a lot of information before sending out rays from the camera. In more simple words, It uses an optimization algorithm to greatly speed up the render time but doing so It is not strictly just modeling the physics of light but it is giving an approximation