So many candidates...
My favourite band is dEUS, but that´s just a weird personal thing, and I won´t try to pretend that they are anything more than that. Best British band for quite some years now: Super Furry Animals. But again, I won´t try to claim them as the best ever.
The Pixies? You can persuade me. Love, I can certainly go with, just for Forever Changes and their version of Little Red Book (which is the best cover version ever). However... Sly and the Family Stone could give them a funk workout for their money, and what´s more they could stick it to the man at the same time as making you dance like a fool.
But, best band - the band I wish I had seen live but never did? Fela Kuti and Africa 70. Seriously. Absolutely intense no holds barred, live it like you talk it, hyper-masculine but not macho, both barrels, brave, loud, proud music that meant something and still does.
*I would use the opportunity the opportunity to write a paen of praise to the luminous, fragile soundscapes of post-industrial detritus and decay, all bleepy analogue synths and sad harmonies that was Grandaddy, but to be fair they were really one person, Jason Lyttle and a rotating cast of supporting musicians, rather than a band.