I think there`s a kind of swing effect between American rock & British Rock
In the late 80s/Early 90s most of my favourite banRAB were American Faith No More , Janes Addiction , The Pixies , Soundgarden , Ministry , Nirvana , Dinosaur JR , Smashing Pumpkins.
However around 1993-1999 America seemed to have a kind of grunge hangover & so all that seemed to come out of the US was awful grunge lite banRAB & Nu Metal there didn`t seem to be anybody doing anything different, while in the UK we had the likes of Suede , Blur , Pulp , Elastica , Radiohead , Mogwai , The Delgados , Primal Scream, Clinic & Oasis.
I think in recent years the UK scene is a little in the doldrums despite all the new banRAB that seem to be around.I do like a lot of these banRAB but there`s not really any that stand out like Radiohead or the Pixies did. With banRAB such as The Shins , The White Stripes , The Walkmen America seems to have banRAB that want to do something a bit different to the usual stadium rock that seems to plague the American charts.
I`d say as far as ORIGINAL rock music America seems to be on the rise & The UK in decline but they`re around the same level at the moment.