I have never been sure on Eagle F1's myself. I know they get great great reviews but then so do Toyo Tyres, and all of those which I have tried to date have been either poor or just ok at best (with the exception of the R888's which are amazing) Proxies are shockingly overrated imo. Ok in the wet but just far too soft for hard driving in dry conditions. May as well have cheese wrapped around your wheels.
RE; Goodyear EF1's
(a) they have a super round sidewall and I always preferred the handling characteristics / aesthetics of the more square Yokohama / Michelin Pilot Sidewalls.
(b) I have never owned a set but test drove a Clio 200 cup with some on before I bought mine, and found them not great on hard roundabout cornering (as in they broke traction too easily).
I currently use Nankang NS2R's for no other reason than they were on the car when I bought it. I have always heard Nankangs referred to as 'ditch finders' in the past, and assumed they were poo. Most probably are, but these are pretty damn good for the money. Best tyre I have used to date (for road and track - by this I mean not a dedicated track tyre like the R888) is the Yokohama AD08R's (R is the newer version for improved wet weather performance). Had these on my Civic Type R and the grip from them is unbelievable, not far off the R888's. They are very expensive but even in the wet they were good. Excellent tyre for these types of cars, considering getting some for the Clio when I need to swap the Nankangs.
Other excellent tyres are Michelin Pilots. Have those on the wifes C2 VTS and they are nearly as sharp as the yoko's were just don't last as well once they get hot.