An air integrated dive computer means one gauge to look at, not two (e.g.: depth, dive time, NDL, amount of breathing gas remaining). One that logs your dives for download to your computer (or smart phone in some cases, I imagine) back home can log your start and end air pressures, calculate your SAC, and thus give you a more full-featured dive log.
Yes, it costs more money. So far, I've chosen to pay it, and I'm glad I did.
I like my Cobalt 2; the compass function is way better than Cobalt 1. That said, if it's been out of production awhile, I'd be concerned it's dated and unless I got a very good price on a used one, I'd probably get a Shearwater Perdix AI or Teric instead.