You havent stated what you want the car for, looks? space? power? tuneability?, what do u want to do with it?
as stated there is a significant price difference, for a really nice 350 track your probably pushing the 45-50k mark, for that price you could get a decent 34gtr, which would be a lot closer in specs than the gtt would be to the 350,
the gtt you could pick up for 17-25k depending on the level of modification, the 350 starts off at a high price.
If you want to be able to take people in the back seat, the gtt can accomodate you, not very well as the rear is quite cramped but the seats are there whereas they are not in the 350, same with boot space.
the 350 is a newer car, so chances are, the ones floating around are in a better condition than a car that is now up to 10 years old, thats not to say that you cant find some nice gtt's with good k's and in great condition,
The point is, everyone on here is going to give you their own opinion, and like it or not, it will be based off what they would use the particular car for, some people like 33's, some people think they're barges... (no offence to 33 owners, i like them but there are people who will say this) it is all a difference of opinion.
FACTS:
350z will cost between - 40-50k for the track model depending on k's and condition
34gtt will cost between - 17-25k, maybe more for highly modded ones which ill assume you probably dont want
350z - is a much newer car, starting production in around 2003
34gtt - older car that started production in 98
350z - 287kw +- at the flywheel
34gtt - 206kw +- at the flywheel
350z - as stated, takes more $$ to push out large figures
34gtt - has a lot of bolt on support to quickly increase power at a low cost
Just a few things to think about, at the end of the day, just think about what you want to use the car for and consider some of the above