I use my phone for a handful of things: (in rough order of priority, but not really): listening to music and podcasts, reading Twitter and Facebook, sending texts via Google Voice, checking email, playing games, reading the web, and making phone calls. There's maybe a few additional tasks I might do, but they're generally of much lesser priority. To break those out:
Music/Podcasts: I never found an Android music player that would do everything I want. To play podcasts at double speed, I had to purchase both a $6 podcast manager and a $4 app for double speed. They worked well enough when they weren't crashing, though the latter used around 40% of CPU, which has a huge negative effect on the already-poor battery (I'll get to this). These functions come with the stock iOS player and iTunes handles the management. There's also a $2 podcast app that does these that's supposed to be more powerful than the free stuff, but I'm happy with iTunes/iOS and can't comment. The best Android player I found was Ubermusic, which costs a couple bucks and was incredibly crashy. Looks and works nice, though. Which isn't a surprise since it's a knockoff of Zune/WP7. I was able to find an app to sync Android with iTunes that worked well enough, and even had a wifi plug-in, however, my phone seemed to have problems staying connected to wifi, so I'd end up having to do it manually (not a big deal, but slightly annoying). The bigger problem is that the Android build I was using had lock screen controls, which is cool, but it seems to be selective about what it controls, and isn't very good at it. For instance, when listening to a podcast in Doggcatcher, the controls would just have a play symbol like nothing was being played. Pressing this would interrupt the podcast and start playing music. I also like the option to use headphone controls, something iOS does out of the box (and even includes (even if they suck)!). Android kind of does it, but seems to forget (for lack of a better term) after you pause. Whether you can even use them depends on the specific phone you get, as well, since not everyone uses the same headphone jack design, and there's no resource that I know of to determine if your phone will work with a given set of headphones. Not so with iPhones. There's only a handful of models, and they all use the same plugs.
Twitter and Facebook: Twitter is roughly equal on both platforms, especially now that it's integrated into iOS 5. Before that I would give a slight edge to Android. The Android Facebook app is not as good as the iOS one, though I'm not sure I can easily explain it. It just never felt quite as polished. This is a wash, really.
Google Voice: Android has a surprisingly small advantage here, but an advantage none the less. Both platforms require you to send via the official app if you want them to come from your GV number, although you can have Android receive in any arbitrary SMS program. iOS is stuck with the stock app. In neither can you send from your GV number in anything but the GV app as far as I can tell. Android's phone calling through GV is better, though, since you can set any arbitrary dialer to use it. iOS requires you to go through the GV app, but it's not that big a deal since your contacts (Google ones, anyway, but that's what I use, regardless) are available in it.
Email: Another wash. They both do it well enough for my needs (provided iOS has GMail set up as an Exchange server), though the Android Gmail app maybe has a better search. It's possible one or the other is better for people who have multiple accounts, but I can't comment.
Games: iOS wins hands down. Android's gaming scene is neither as large nor as high quality. I had a *really* hard time finding anything free of any quality on the Android Market, while finding them on the App Store is pretty simple. (It probably doesn't help that the Android Market is not that easy to search, surprisingly.) Not that there's nothing of quality on Android, but it's largely ports of old iOS games. My completely uninformed guess about this is that development is more difficult on Android due to the sheer number of phone configurations available.
Web viewing: Android mostly wins here since you can find alternate browsers and set them as default. There's alternate iOS browsers, some very good, but you can't set them default. Safari is perfectly adequate for light browsing, though. Android has Flash, but my few attempts at actually checking Flash sites on my phone didn't really convince me that it's a *good* thing.
Phone calls: Wash. Both sync with Google contacts without a problem. The dialers are fine on both. The above Google Voice issues exist. Slight advantage to Android in that T-Mobile has free wifi calling, but I use so few minutes, that even the basic plan I now have on Verizon is far more than I need in a given month.
Other stuff: iOS comes with a bunch of stock apps that seem to not be in stock Android (calculator, weather, stocks, notepad), but this is easily solved via the Android Market, so I don't really consider it a big deal. It's a strange oversight, though. I assume the various manufacturer custom versions (Sense, Blur, Touchwiz, etc.) have these things.
Battery: This is, of course, going to vary by phone, but with similar usages on my current iPhone and old Android phone, the iPhones wins by a good margin. On a work day, the phone comes off the charger at ~7:30AM, I take the train to work and listen to podcasts until I run out, then listen to music for most of the day, and take the train home. On Android, I had a utility that turned wifi on and off depending on location and if I remembered, I'd just put it in airplane mode while underground. On iOS, I just leave it all on. On my G2x, I'd be under 30% around 4PM at the latest, meaning I'd have to charge at work (not a big deal, but I'd prefer not to) while with the iPhone, I can make it home (~6:30PM) with 35-40% available.
Some other thoughts: iPhones are the top selling smartphone on the market (iPhone 4 was the top selling smartphone for AT&T and Verizon April-September, and I doubt the 4S will break this trend) though Android has the greater share of the OS market. While I don't have any dog in the sales race, more iPhones does mean more available accessories and more integration with other things (car stereos, home receivers, etc.), which does affect me. As I said, Android does some things very well. I liked the breadth of customizations. The previously mentioned wifi utility is nice. The ability to put controls for things like wifi, cellular data, and so on on the homescreen is very handy. The variety of hardware is nice in that it gives people options, and that's not a bad thing. Want a hardware keyboard? There's probably an Android phone for you! No iPhone though, sorry! I like the ability to expand storage, but that seems to be slowly going away. This does lead to the issue of now having a directory structure to deal with. My G2x came with 8 GB internal and I stuck a 32 GB SD card in it. Great, 40 GB of space! Well, sure, but not contiguous, and it therefore necessitated telling individual apps where to save. Not a huge gripe, but kind of pointless. Switching batteries is theoretically handy, but I'm usually not away from outlets long enough for it to matter (and this, again, depends on the phone).
EDIT: A big one I forgot: Updates: Apple has released one big iOS update each year (though there's a possibility that could slow a bit to 18 months, but that remains to be seen) and a number of smaller bug updates with an occasional new feature in the interim. They've traditionally been putting the updates on anything up to two generations older than whatever it was released with, albeit not always to great performance (the iPhone 3G didn't much like iOS 4, though the 3GS is reportedly fine on iOS 5). Currently, this means Apple is still officially supporting a 2.5 year old phone. Google, similarly, releases one or two major updates per year (if we, like the majority of the market, ignore Honeycomb, which is essentially a beta for ICS, anyway, and also define 2.0, 2.1, 2.2, and 2.3 all as major updates, which is arguable), with a number of smaller bug releases with an occasional new feature in the interim. However, getting from Google to a given phone is a much bigger process involving the OEMs hacking it to run on their handsets (remember, Google only codes for the Nexus phones - every other handset on the market is derived from this), often with some user interface stuck on top that is really great at using system resources so you can have a giant clock taking up half your home screen (in addition to the status bar clock). The end result of this is that there's no guarantee when or even if your phone will get the latest release unless it is a Nexus phone. There's brand new handsets being released with 2.2 despite 2.3 being nearly a year old. A number of very capable year old phones (the US Galaxy S line comes to mind) have yet to receive official 2.3 updates. So the obvious choice is to just get a Nexus phone, except that there's *still* no guarantee that you will get updates more than a year out. Google has officially stated that the Nexus One, a less than two year old phone, will not be getting the ICS update. So basically anyone who bought one on contract will have an unsupported phone before the contract even ends. (I will grant that Apple is still selling new 3GSes today which will certainly not be supported when that contract ends, but I will also say that anyone buying a 2.5 year old phone just to save $100 (or, more accurately, $4.16 per month of contract) needs to seriously reconsider holding off a month or two to buy something better.) It's a pretty sorry state of affairs. You can argue that this can be solved by using custom ROMs, but, frankly, I think that's a really, really poor solution and something most people aren't willing to do. I did it, and it ultimately ended up being far more of a hassle than it was worth, and there's never any guarantee that the developers will ever be able to enable all phone functions due to various things.