Time for some sweeping generalisations.
Rock = Tough to choose between the US and the UK. If you prefer the heavier stuff you might lean towards the US but if you like old school rock then you'll probably give it to the UK. EU belongs in the bin.
Hip Hop = US annihilates everyone although currently UK Hip Hop is probably truer to Hip Hops original routes than the autotuned mumble rap which now dominates in the US. EU again belongs in the bin.
R&B = Easy US win, UK second, EU...
Jazz & Blues = US wins again, UK very distant second, why am I even bothering with EU at this point ?
Electronic Music = UK win with EU finally putting in a top effort as well. The US played a pioneering role in the formative years at an underground level but it never took off in a big way until the mid-late 2000's when it go rebranded to yanks as 'EDM'. The US takes a hard L here.
Overall the US wins on depth of genres but id perhaps argue that the UK's peaks are higher. EU is good for obscure pretentious electronic music and not much else.