What's the difference between Burt force and Light cash in Vray render engines?

The best way to tell the difference is to try both and compare results

check this site http://help.chaosgroup.com/vray/help/200R1/examples_GI.htm

It has good examples of using different engines, including the time it takes for both render.

For me, irradiance map and light catche together do wonders!! That's after years of trying different settings. They provide good results inreasonable timing.

Brute force - this is the simplest approach; indirect illumination is computed independently for each shaded surface point by tracing a number of rays in different directions on the hemisphere above that point.Advantages:

• this approach preserves all the detail (e.g. small and sharp shadows) in the indirect lighting;
• it is free from defects like flickering in animations;
• no additional memory is required;
• indirect illumination in the case of motion-blurred moving objects is computed correctly. 

Disadvantages:

• the approach is very slow for complex images (e.g. interior lighting);
• it tends to produce noise in the images, which can be avoided only by shooting a larger number of rays, thus slowing it even more.

Light cache - light caching is a technique for approximating the global illumination in a scene. It is very similar to photon mapping, but without many of its limitations. The light map is built by tracing many many eye paths from the camera. Each of the bounces in the path stores the illumination from the rest of the path into a3d structure, very similar to the photon map. The light map is a universal GI solution that can be used for both interior or exterior scenes, either directly or as a secondary bounce approximation when used with the irradiance map or the brute force GI method.Advantages:

• the light cache is easy to set up. We only have the camera to trace rays from, as opposed to the photon map, which must process each light in the scene and usually requires separate setup for each light.
• the light-caching approach works efficiently with any lights - including skylight, self-illuminated objects, non-physical lights, photometric lights etc. In contrast, the photon map is limited in the lighting effects it can reproduce - for example, the photon map cannot reproduce the illumination from skylight or from standard omni lights without inverse-square falloff.
• the light cache produces correct results in corners and around small objects. The photon map, on the other hand, relies on tricky density estimation schemes, which often produce wrong results in these cases, either darkening or brightening those areas.
• in many cases the light cache can be visualized directly for very fast and smooth previews of the lighting in the scene.

Disadvantages:

• like the irradiance map, the light cache is view-dependent and is generated for a particular position of the camera. However, it generates an approximation for indirectly visible parts of the scene as well - for example, one light cache can approximate completely the GI in a closed room;
• currently the light cache works only with V-Ray materials;
• like the photon map, the light cache is not adaptive. The irradiance is computed at a fixed resolution, which is determined by the user;
• the light cache does not work very well with bump maps; use the irradiance map or brute force GI if you want to achieve better results with bump maps.
• lighting involving motion-blurred moving objects is not entirely correct, but is very smooth since the light cache blurs GI in time as well (as opposed to the irradiance map, where each sample is computed at a particular instant of time).