Supra is cheaper to run, cheaper to maintain, cheaper to modify & more reliable.
The GTR is better at everything else. It also makes a (slightly) better noise, handles better & has useable rear seats. I also prefer the interior & the exterior looks of the R34 over the Supra.
My Supra is definitely faster than the R34 & I have the added bonus of not expecting to end up on the back up of a trailer every trip - The unreliability issues took a lot of the fun out of driving it/Owning it. My Supra is more powerful than the GTR though (GTR just had filters, downpipe & exhaust).
In terms of driving they are difficult to compare, The GTR is a lot more planted (Especially once you ditch the HICAS) but the Supra is more fun to drive - It reminds me a lot of my supercharged 350Z.
In an ideal world I'd have both, but the R34 is the one car that I absolutely need to own again at some point in my life - There won't be another Supra after this one