That's what I was aiming at. Take a corner @ 60 km/h on shit tyres = poor handling. Take the same corner at the same speed on stickier tyres = better handling. But you still need to look at the other aspects.
On the flip side, you can have an awesome suspension etc. and have crap tyres, and still get poor grip. But it depends on what you want from your car though (seeing it's a GT-R, I would say, the higher the grip level, the better).
To me, it sounds like the OP's suspension is too stiff and low, with standard-style wheel alignment settings/stuffed up alignment.
What wheels do you run Luke?