For WRX I would go performance:
1. Michelin Pilot A/S4
2. Continental ExtremeContact DWS06+ (I have them for late spring-early to mid Fall).
3. Bridgestone Potenza Sport A/S.
4. Pirelli.
Those 4 brands will have overall most balanced performance.
Performance tires have different compound, stiffer outer blocks to provide better, more precise handling. Emphasis will be on dry and wet, but the reason why I use performance A/S tire instead of summer performance tire, considering I have snow tires, is that in between period when it gets cold, then hot, then some cold rain etc. Those performance A/S tires still keep flexibility and will get you through some light snow.
Problem with grand touring tires on car like WRX is that car has more potent suspension and brakes (although I didn’t hear a lot of positive things about WRX brakes) that might be too much for tire performance. Grand touring tires will have softer side blocks, less precise handling, less feedback on steering wheel, not as good braking(remember, brakes, handling, AWD etc. are only good as tires are).