I am not a hater or a basher or jealous or afflicted with schadenfreude but Neil's drumming has never done it for me, despite the fact that he's obviously a world class drummer. It's only my opinion and the huge number of people who love his playing is testimony that his playing does touch people - just not me.
I suspect the qualities in his playing that don't touch me are part of why some people don't fancy his big band playing. In both rock and jazz I find his playing a bit clinical for my tasttes. Not only his approach but also his sound. The thing I like best about jazz drumming is the sound - all those subtle nuances where the players extract lots of sounds from each part of the kit. When coupled with dexterity, it creates an organic sound that I enjoy. I don't hear the subtleties in these takes - just very clean execution with some dynamic sections. I would like to hear more sounds extracted from the ride, a more open, higher tuned snare (less of a pinstripe-y sound), same with the toms.
As a drummer I'm barely qualified to carry Neil's stick bag - it's just how I hear it.
Some might find it a bit rich for a Bill Bruford fan to call Neil's drumming clinical, but Bill was so imaginative in his use of sounds and general approach - most times it's bright and colourful.