My wife got an iPhone a few months ago, and I have to admit to being taken by it. The still and video camera are phenomenal, even regardless of their physical size. It takes better HD video than our Sony HD camcorder. The user experience is more streamlined in my opinion. I've had Android phones for 3 or 4 years and they've always performed pretty well, but you have the ocassional lock-up, the hang, the crash, the force close, etc.
The differences between iPhones and Android phones, in general, are becoming smaller, at least as far as hardware goes. I was always a critic of the iPhone's lack of removable battery and lack of SD card bay. As it turns out, fewer and fewer Android phones have these features these days. To me, that was one of the big advantages of the 'Droids. Then again, you never really have to pull the battery on an iPhone because it's generally very stable. My wife has never reset hers, in the 3 months she had it. Her previous Droid 2 had to have a full factory reset about every 6 weeks because it'd repeatedly lock up and would no longer recognize the keyboard.
Yesterday, I upgraded to an iPhone. Like any new phone and new experience, there's a lot to like and a lot to play with and explore. The screen quality is outstanding, the user interface is extremely well thought-out, and the hardware is superior in construction to any other phone I've held. If you like that aspect of something, the engineering, the feel, the construction, you'll like the iPhone. If you like customizing phones and rooting them and things like that, you'll like an Android.
My brother had an iPhone 3GS and moved to Android a few years ago. He's now on a new Google Nexus (that new one that keeps dropping calls) and he says he might go back to an iPhone.
I personally don't think one is "better" or "worse" than the other. Each will simply SUIT different users better or worse than another. Kind of like Ford vs. Chevy. Both are fine vehicles, but some people just seem to like one more than the other, and for any number of good reasons. Android and iPhone is the same way in my opinion.