From a purely taste standpoint, I go the GT-R. I've been fortunate enough to experience both GTRs and Supras - and I really like the motor and drivetrain of the Supra, good, strong, and easy to make good power from. However, I really don't like the package.
To me, Supras lack any spirit... they feel and look not quite all there to me, very hard to describe - which is why I emphasise this is purely from a taste perspective. They are very very good cars, and go incredibly hard - awesome power delivery, good handling, good brakes etc.
However, with a GT-R - despite people saying they look plain (to me Supras look like someone have been designed by checklist - "Got scoops? Got wing? Got arches?etc OK - we have a sports car..."), where as *GT-R*s have a certain presence to them. They aren't something that is trying to be a big means sports car, they are a touring car that is pumped up on steroids and ends up just having a staunch presense.
GT-Rs *feel* like something a bit special - they rev and sound more exotic than 2JZs (not talking about performance, talking about driver impression), they sit on the road a certain way, they have the "look at my afterburners" thing going on, spit fire whenever there is the need, and have ludicris amounts of traction yet will still powerslide and powerslide (and then bite) in a way no RWD Turbo will do so. They are quite a lot of fun for a barge