This is actually something where I've switched a lot compared to when I first watched the show. Initially I liked OP3 the most. 3>1>2>4 I hated the Engrish so much in the 4th one and thought it was way too overhanded. I've kinda come around on it. Now it's 1>2>4>3. Mostly due to how bad the animation is in the 3rd OP.
I think I hated the 3rd OP because of the screamin'. I can deal with plenty of different things in anime music, but I dislike screamin'. Kinda why I disliked "I COTIBUE TO FAAID I COTIBUE TO FAAAAAAID." In Code Geass' R2.
Personally I feel like the first two OPs for E7 are just awesome as fuck in general, the fourth is probably the weakest but still pretty good, and the third OP is a weird case: the actual full single version is probably my favourite of all the OPs, but the version used in the show sounds pretty goddamn awful in comparison and may actually be my least favourite.
EDIT: Also, it just occurred to me that it seems bizarrely appropriate that Corvo's been watching Eureka Seven, Code Geass and Madoka in such close proximity, since those are the three series I've made English versions of the OPs for over the years. I already linked Connect earlier (and I think that's the one I did the best job on), but the other two songs I did years before that were COLORS and Taiyou no Mannaka e.