i've run in adidas and they're comparable to nike. the supernova is the really lightweight running shoe, right? (it's been a long time.) if they don't bother your feet, who can argue with free shoes?
personally, i like new balance, and when i was wearing asics, i'd wear down the sole, (terrible, i know!), long before the 'mileage replacement suggestion' took effect. i absolutely loved them, but didn't want to keep replacing shoes in half the time it 'should' have taken. that, however, was probably 10-13 years ago, so things might be better now.
brooks makes a good shoe as well.
a lot of runners tend to stay more toward the brooks, asics, new balance, saucony side of the house when choosing personal running shoes.