I succumbed to the overwhelming advice both here and elsewhere and went for Michelin Pilot Sport 4 tyres for my 17 x 8 wheels. So I replaced a rather good set of Falkens with same-size Michelins. Here are the exact tyres:
Falken Azenis FK510 225/45R17 94Y XL (£75.10 each)
Michelin Pilot Sport 4 225/45R17 94Y XL (£83.51 each)
My impressions as follows (I don't track my car, it's my daily driver used in a 60-mile commute):
Noise: the Michelins are definitely quieter with less tyre roar into the cabin.
Dry cornering: I can't feel much in it although I haven't pushed the Michelins hard yet.
Wet cornering: on this morning's greasy roads, cornering while applying some throttle made the rear just start to move sideways. The Falkens would have held fast doing that.
Dry stopping: seems ok so far, no emergency stops yet for me to compare.
Ride quality: there isn't a lot in it although I think the Michelins are just a bit firmer. Both tyres suit my H&R Super Sport springs well, the ride being firm but supple.
Looks: meh, I don't really care how they look.
I thought I'll add to this as time progresses and I get used to the Michelin's limits. The price difference is not huge so this doesn't feel like a criticism of the Michelins so much as praise for the little known but excellent Falkens. One parameter that will definitely have to wait a while is life. This may be where the Michelins win (the Falkens were on for a year or around 15,000 miles).