While I've not driven on all of the tires on a GTI, I've run through several sets of different things on my Mazda2 which was my previous track car (and was autocrossed a lot prior to discovering track things).
Bridgestone RE71R (I burned through 2 sets) - Awesome grip for a lap or two, then get greasy. Great for autocross, great for time trial track stuff... not great for doing repeated lapping. Also sucked because they wear stupid fast. They have a very "sharp" feel where you can tell they're breaking traction laterally. Definitely rewards smooth driving generally speaking. Funny enough I found it more cost effective to run a set for about half their useable life, sell for 50% of the original purchase price to someone, and buy another set. When I was autocrossing it literally cost me the same to buy two sets for a season and always be on "fresh" tires than try and stretch a set of one all year (which was definitely doable with regular rotations and flipping on the rim). Awesome in the rain as long as it wasn't deep standing water. One of my sets I used for autocross, it was on these tires I did my first HPDE weekends and then proceeded to burn the second set up doing the same.
Hankook RS4 (3 sets) - Wears like iron and lasts easily 3-4x as long as RE71Rs. Terrible for autocross unless it's stupidly hot out AND you had a codriver. They're still not the fastest but they're not as bad relatively speaking. Back to TRACK things: they were maybe 0.5-1.0sec slower on a 90 sec road course vs RE71Rs, BUT they could do those laps repeatedly ALL session long never falling off. The RE71R would have a flyer lap and then slow down to roughly the same overall speed. These tires feel like crap unless you have them stretched on the wheel. Also these things run WIDE. I ran 195s(which actually measured WIDER than 205 RE71Rs) on 8in wide wheels, and 225s on 9in wide wheels. If you can make them work, or don't care about the "fastest" time possible, these things are a great tire if you're on a budget, or drive on an abrasive surface, or have a lack of camber with no desire to add more. Really sucks in the rain, but nowhere near as bad as BFG Rivals. Predictable breakaway, just low limits in the rain.
Falken RT660 (2 sets) - Very similar overall feel to RE71R. Within noise of the RE71R time wise overall (comparing a flyer lap from RE71R only), but does not get greasy anywhere near as quick. Typically good up until tail end of a 20 min session. Wears somewhere between the RS4 and RE71R. Not quite as good as the RE71R in rain, but also not as bad as the RS4. Honestly I really like these as a happy medium for doing everything well enough. I bought a set of 245/40R17s for my GTI and had no complains of them at VIR a few weeks ago.
No comment on anything else, though I've driven a bunch of other tires just on different cars and/or not for enough laps to make a fair judgement call.
edit: I will add that because my car only made 97 wheel horsepower… Forward traction was not exactly something ever really being tested to the limits except in the rain. The RS4s were probably worst of the bunch in that circumstance though. I also just remembered that the RS4s I ran were 195/50R15 vs 205s for everything else. In ACTUAL size comparisons the 195s were a tiny bit wider than 205 RE71Rs, and 0.6in shorter overall. I suspect gearing came into play and if all sizes were truly equal, the delta between them and the others would be a bit larger.