The difference is many things, but mainly the feel and overall performance, the Dayan cubes are the ones that does not look anything close to a Rubik's brand, while the FII is similar to it, most of the type A's are known to be more clicky in their feel, while type F cubes (except F-III) got a smoother feel.
In my opinion no cube is the best, depending on my mood and my hand condition different cubes tend to be better for the situation than others, but I mainly stick to my ZhanChi when cubing in more public places, mainly for having extremely low risk of pops, but the Guhong got a awesome feel too, but nothing beats the F-II IMO, C4U also got a nice feel, but it locks and pops too much to be enjoyable when speedcubing, for casual it's pretty neat though.
To identify your cube without taking pictures, snoop around until you suspect what cube it is, then google: *Cube name* pieces
That should usually give you a decent look at the pieces of the cube you specified.
Other than that, I can't help you, and now I'm off to bed ~_~
