The advantage of the 64-bit version is using the 64-bit capibily of a 64-bit processor like using 4GB and up of RAM. The 32-bit version supports just a bit less then 4GB of RAM.
The disadvantage is that you need 64-bit drivers and not all manufactors have released them. Also 16-bit programs aren't supported (Which isn't a problem if you don't have any, only programs from around 1995 would be 16-bit anyway).
If you don't need a lot of RAM and you aren't using a lot of programs then it's best to stay with the 32-bit version for now.

As it is a laptop and is being supplied with Vista64 or 32 (unless it is a custom build) the drivers will not be a problem (as the manufacturer will have released them).
You could probably run most of those pre 95 16bit programs in DOSBox if you are desperate.