Type B cubes are one of the inferior DIY types. Oddly enough, many of the more 'exotic' cube colors are of this type, such as transparent cubes. They can be used in hybrid cubes, for example Erik Akkersdijk (world record holder) uses type-B cubie's with a Rubik's DIY core.
Type F cubes are different in that instead of having caps on the inside of the pieces (as all cube pieces are hollow) they have caps on the OUTSIDE so as to keep the rubbing surfaces as smooth as possible. Unfortunately, the core is of bad quality, and deteriorates quickly after lubing. It can be replaced with an A core and improved. Type F cubes often considered to be the smoothest cubes on the market. They turn relatively fast and are used by some speedcubers.
Type-F II cubes are widely considered to be similar in turning quality to the Type-F, but without the drawbacks of Core deterioration. Many cubers use this cube. The cube has the curious characteristic of slightly rounded cubies and edges that are truncated and capped. The rounded cubies cause average 3x3 stickers to be just under 1mm too small. This cause tiles to extend out from the cubies a little. The truncated edges are presumably to reduce friction in the cube and prevent the edges interfering with the core. This cube is quite light compared to other cubes, which coupled with the smooth turning gives the cube a delicate feel.
