I've been using the Google Hangouts app on the iPhone since it was announced on Wednesday, and I've really liked it so far. I haven't messed around with it much on my iPad, except to install it, but it was enough for my Android-using husband to be jealous that we got it first.
Like Apple's Messages, it's pushing conversations to my iPhone when I'm not at my computer, a feature which I've grown to love in iOS and OS X. The Hangouts app has a great feature to snooze notifications, which is great if you're going to be at the computer for awhile and don't want the iOS app constantly alerting you to new messages. However, there's no way to change your status and alert people you're having discussions with that you might be out of pocket for a bit, but it's something that's not in Apple's Messages either.
The biggest missing feature in Hangouts is SMS integration, and Google vows it's on the way. Google community manager Dori Storbeck said the feature was the most-requested one and is coming soon.
However, as TechCrunch points out, the SMS integration most likely will be Android-only because of permissions limitation on iOS. It's a shame, because I wouldn't mind having some Hangout messages default to texts if a reliable data connection isn't available.