I own both, and I've been swapping back and forth. I have a Samsung Galaxy S2 and an iPhone 4. I bought the SGS2 mostly because I need an unlocked phone and I saw a good deal on a used one.
There are things that I like about both, and I thought Poofyhairguy did a good job pointing them out.
On the Android side, I generally like the customization, although I don't use it much myself. I love the notification system. I love the screen on my SGS2 and the ability to use SD cards. I like the feel of the phone itself much better than my iPhone. I like certain apps - like Google Voice and Amazon's Kindle app - much much more on Android.
On the iPhone side, I like the integrated backup system in iTunes, I like having a button to start speech recognition on the phone without looking at it, I like the fact that everywhere I go (hotels, etc) lots of devices are built to take iPhones and so charging is generally easy, and I like that the earbuds have a digital volume control built into them. And there are a few apps on the iPhone that either don't exist or are substantially junkier on Android that are apps my kids or I use a fair bit.
Overall though, I find it pretty easy to swap back and forth and that's a sign that things are more even than most people seem to say they are. The truth as I see it is that the two platforms are generally pretty equivalent. You don't need to jailbreak (I haven't in years), you don't need to root (I haven't yet, although I did install CWM).
I'm thinking my iPhone is going on Ebay... but there's still a few things that I don't like about Android. Like it still chimes when I plug in USB, it still wakes me up at night to tell me that it's fully charged, and I've found the bluetooth on the SGS2 to be slightly buggy in my car. It will just drop occassionally. No idea why. Could be the phone, could be my car. But beyond a few annoyances, I generally find that I like Android.
I agree with the advice of going and playing with both in person and seeing what you like. I'd advise someone to do some common things on both and play around a bit.
I personally don't think you can go wrong with either platform.