Many thanks for all the quick and helpful replies, guys!
So, lots of support for the Michelins. Not surprised, as I've read lots of favourable reports elsewhere, and Michelin are one of my favourite makes too.
Like the Goodyears, they're rated highly for wet performance, fuel economy, etc, but there's one area where the Goodyears have a clear advantage: noise. They're supposed to produce just 69 decibels, against the Michelin's 72. Apparently, because of the logarithmic way the decibel scale works, that actually means the Michelins produce twice as much noise as the Goodyears! (I know - sounds implausible, but pretty certain I've got it right.)
That's not to say they're at all bad (72-73 seems pretty typical, even among the more expensive tyres), but the Goodyears do seem particularly good in that respect (seem to recall only the similarly-priced Bridgestones come close).
As the existing tyres make quite a racket (especially the Generals on the front), it's something we're a bit sensitive about.
Still open to thoughts on tyres, though, including on the issue of 205/65 v 215/65.
I gather the slightly taller sidewall on the 215s (I know the second figure is a percentage of the first, not a measurement in itself) is reckoned to give a slightly softer ride, but I wonder if the extra few mms makes a noticeable difference? I can see there'd be a little more grip, too, but a corresponding drop in mpg as well.