Don't have my GTI long enough to comment on it specifically but precisely owned an audi TT which was always shod with Pirelli p zeros which I found excellent if a little soft wearing. Shortly before I sold it I stuck 4 budget tyres on it cos I knew i was changing it... It went from being a cat I really enjoyed driving to one I dreaded getting into every day. Grip was atrocious wet & dry and led to many butt clenching moments. Lesson learned!!
Also have experience with F1's which were great wet or dry. My GTI came with 4 new p zeros & hair enough with them so far but getting used to the car. Might look at the michelins after these going by this thread.
Either way long story short.... Don't go budget, you will regret it. Even if you don't meet the ditch you'll hate the driving experience.