Generations are
1 - Smooth grip
2 - Textured grip
3 - Finger groove grip and rails
On some compact models there is a "generation 2.5" which has grooves but no rails. My G30 is one such.
I am not an expert on the G35 but it's a fairly new model so doubt it would have too much chance of being anything but 3rd gen, which was phased in IIRC around 1997-2001.
EDIT - the G35 was introduced in 1998, so may be a Gen 2 possibly, although I suspect for a new model they went straight into Gen 3. Just a guess though.
Adavantages depend entirely on whether you want a grooved grip or a rail. Only other thing to watch out for is some EXX serial numbers had a frame recall issue and that's within the lifecycle of the G35. Glocktalk has a bunch of stickies on this issue so check them out if you have any worries there.