This is a surprisingly hard choice.
Blur -- I admire Blur for several things: 1) being creative and dynamic in style (much like U2) when their peers were reinventing the same wheel over and over; 2) having a really good guitar player (Graham Coxon); 3) being survivors -- the British music press (surprise, surprise) wrote them off in 1993, and again in 1996... but they always came back stronger; 4) not feeling any particular need to break in the US-market -- not that there's anything wrong with doing so, but I like that Blur didn't ever pander to MTV or American stadium rock expectations (Liam Gallagher, by comparison, posed on the cover of Vanity Fair magazine in the US after Albarn refused to do so).
Now, for the prosecution: 1) Although they were creative, Blur were never original. They started out as Baggy scene-jumpers, then became 60's-style Kinks Brit commentators, then became post-everything low-fi indie rockers... Albarn always seemed to be looking for a new style to copy; 2) Damon Albarn -- the most pretentious of all 90s' Brit stars? (and that's saying something.) I cannot stand him. Saw him recently on Canadian TV -- he was more pretentious than ever, and seemed even more self-obsessed and defensive. 3) Albarn's voice -- I cannot stand his shrill voice on many Blur tracks, though occasionally he gets it right when he tones down the hammy histrionics; 4) Blur's songs are very hit and miss. You maybe get 1/2 good tracks and 1/2 crap on the average over-long Blur album.
Oasis -- Oasis are the one whose catalogue I'm most familiar with (I also saw them live in London in 2000). The first album is very good, but not brilliant -- largely because it lacks any diversity and every song sounds exactly the same. The second album is weaker, but still very enjoyable in a dumb kind of way with big tunes and hits -- it even broke down the US market. At that point they became the uber hype of Britain for all of 1996 and 1997, and the third album is a stinker -- 4-chord songs with unimpressive playing that drag on for 7 minutes, and the worst lyrics of any LP I've ever heard. At that point, the original line-up was pretty much done and thereafter Oasis became a caricature of themselves, something that they seemed to enjoy (perhaps showing how insincere and false they were in the first place). Mediocre LPs like Don't Believe the Truth (oooh! clever title!) are fawned over by their Dad-rock fan base who think anything vaguely in tune and in time and with a 60s' flavor must be classic Oasis.
Oasis did what they did very, very well -- they did loud, anthemic dumbed-down no-funk, no-swing rock'n'roll songs, all in exactly the same style. If that floats your boat, they're for you because nobody else does that better than them. But that is all they do.
(The) Verve -- The Verve have the most American-friendly sound of the three, I think, and also the best singer. Their first two albums are very interesting, and then the third is a lot more song-based and was deservedly a massive international hit. After that, they were more-or-less cooked, but of course they've had a little comeback. It's harder with The Verve to identify what exactly they do, because their first three albums (the "real" ones, if you will) are all quite different. The first one is way out there in artiness, the second more cohesive but still arty, and the third is almost a Richard Ashcroft solo album backed by The Verve and has succinct, tightly-written rock/pop songs. I like what they did but they didn't really do a lot, I suppose.
So, in conclusion, I can't answer the question.