R33 and R34 are pretty much the same. Being general here! Not going into specifics.
GTR has the RB26DETT twin turbo engine and active 4 wheel drive. 276bhp standard.
GTS has the RB25DET single turbo 2.5 litre engine with 250bhp standard (more like 230bhp though) and rear wheel drive unless it's a GTS4 which has permanent four wheel drive. Also there is a RB25DE that has no turbo.
GTR's are much nicer inside, have better suspension, different gearboxes, better brakes, ABS etc. ABS is optional on GTS's. Also the bodywork is different on all models. R32 onwards, the GTR's have flared front and rear wheel arches, bigger bumpers, different spoilers etc.
Depends what you want really. If you only want around 350-400bhp then you may as well just get a GTS and spend a bit of money making it look better. GTR's are easier to get big power, but if you're like me a GTS is a better option. Cheaper to buy, run etc.
To be honest both very fun to drive but completey different cars. Come to a track day or a meet and I'm sure someone will take you for a spin.
Whatever you get there is always lots more you can do to it. I've got a GTSt and I love it. Rear wheel drive, no traction control, no LSD, no ABS and 342.5 BHP. Oh and as far as torque goes...326 ibf/ft so its quite torquey
GTR does look more the part, where GTS tends to look more like a family car.
Most people when talking about the R33 GTS say they are only available with the RB25DET or RB25DE engines, don't forget about mine though !, it has the RB20E engine, 2.0 as opposed to the 2.5 and single overhead cam as opposed to the twin cam jobbie.
Visually they are all the same and you cannot tell the difference from the outside apart from the 'GTS' 'GTS25' or 'GTS25t' badge's on the back (and the 16' wheels on the Turbo), interior wise, again, all exactly the same apart from a boost gauge on the rev counter on the turbo version.
All are excellent cars which vary on performance depending on what version you have (and how deep your pockets are !) and all are VERY tail happy in the wet !!!!!