January 14, 2011: Updated with more!
(This post is forever "under construction")
I have owned an iPhone 1, an iPhone 3G, and an iPhone 4. This fall, I moved to a new office in downtown Manhattan. Suddenly, I was unable to make or receive phone calls in most places. Also, 3G service got terrible. So basically, my iPhone became an iPod Touch with a steep monthly fee. So I gave it up for a Motorola/Verizon/Google Droid X. The Verizon service has been great. Here's my personal take on what's better about each one.
Where Droid beats iPhone
(New!) FlashThis is a big one. The Droid runs Flash. Without Flash, lots of sites just don't work, or don't deliver their full content. I've read Steve Jobs's reasons/rationalizations for not supporting Flash on iOS, but it runs on Android, and so far the world is still in one piece.
Verizon cell and 3G serviceVerizon's network is a joy to use, reliable all over Manhattan and there when you need it.
ScreenDroid's screen is larger, making web surfing a lot more pleasant.
Sync with GoogleDroid syncs out of the box with Google contacts (iPhone can be set up to do this).
Organizing appsDroid keeps your apps in alphabetical order.
(New!) WidgetsI like the wide variety of widgets Android has for customizing the home screens. Some of my favorites -- One-touch calling, TweetDeck, bTunes, Facebook, and Pure Calendar.
Where iPhone beats Droid
Calendar appOn Droid, the calendar app has odd bugs - it scrolls in unpredictable ways, and switches your view without warning. iPhone's calendar app just works and is much easier to use.
UPDATE - CalenGoo for Android (about $6) is pretty good. Why are the apps that come with Android so god-awful that we need to pay to replace them? I think it's because Google doesn't make any money directly from Android, so they just make the apps "good enough". Apple's reputation is riding on the user experience of the iPhone, so they take care to make it great.
Calorie counting appEdibles for iPhone is better than anything on Droid.
Front cameraiPhone's front camera is indispensable for taking pictures of myself, whether for uploading an avatar or for vacation photos.
Built-in music appiPhone's iPod app is much better than Droid's Music app. Droid's app skips, plays album tracks in alphabetical order (!) instead of the artist's order, and loses album art when loading your music. On the Droid, I would recommend MixZing (free). bTunes ($1.49) is also good; its interface is a clone of the iPhone's music player. UPDATE - These apps don't support podcasts, so on Android you need.. guess what.. another app.
iTunes StoreAndroid has no built-in music store. [UPDATE - A friend told me that Android has the Amazon MP3 store. Not very obvious, but it is there.]
New York Times appBoth phones have one, but on the iPhone, you can update all sections of the paper at once, while on Droid, you must update them one at a time. This is significant because my newspaper downloading time is a few rushed minutes in the morning before I get on the subway.
Push notifications to the home screeniPhone has them, Droid does not. Result: I often miss text messages, and I don't get Foursquare or Twitter messages as easily.
BackupThe iPhone backs up data and apps to the Mac out of the box. Droid's over-the-air backup doesn't seem as trustworthy.
Game selectionThere are far more games available for iPhone than for Android.
Uploading photosOn the iPhone, photos sync with iPhoto out of the box.
New, cool appsMany apps are first (or only) on iPhone. For example, the Chase bank app that allows you to deposit checks on the iPhone by photographing them - not on Droid.
User Interface and navigationI would give a slight edge to the iPhone due to its lack of hardware buttons. On Droid, the buttons hide functions and force you to guess where things are.
Killing TasksOn the Droid, you have to constantly manually kill open programs or the battery drains quickly. iPhone does not have this problem. [UPDATE] - Tom, in a comment, says that Advanced Task Killer can do this on a schedule. I wasn't aware of the scheduling feature. Thanks! Still, this should have been a built-in OS feature, not an app.
App storesBoth have good app stores.
Still camera and video cameraVery good on both.
App updatesBoth can update apps using wireless, which is convenient.
Bread and butter appsMany apps are the same or equivalent on both platforms.
App reviewsBoth app stores have user reviews.
Sorry, Droid! You have geeky cool, but when it comes to real use, the iPhone wins.