Guaranteed, Sims 3 gives you the better game experience (it's just more fun in my book than sims 2 but of course that's purely subjective)
If sims doesn't play right, it's in 99% either missing RAM or an insufficient graphics card.
You say Sims 3 runs on your Laptop.
Seeing how the requirements for Sims 3 are higher, Sims 2 should work as well.
You just get a gray screen...no error message...no Sound? Have you tried to ALT-Tab out of that window (in order to minimize it) ? Those Error messages have a habit to hide behind the window sometimes.
If the game ever ran and you get that screen at a subsequent start, you need to delete the game caches for it to start again