I'm liking the current momentum behind Android. I'm sure Apple will come out with their new phone soon, and the pendulum will swing a bit, but it's definitely a two horse race, and Apple isn't out of sight, not by a long shot.
I got my Nexus One from http://www.google.com/phone a few months ago, to replace my aging K800i (which still takes better photos than the Nexus One, or the iPhone, or indeed most phones). Since I got my phone directly from Google, it was easy to update to the latest Froyo, which got rid of some of my bigger annoyances on the device. Most tedious in previous versions was the need to individually select and authorize every application when an update showed up. Most days I see between two and five updated applications, and updating any given application takes around 30 seconds, so it was turning into a chore. Froyo is also much smoother in its transitions; it's the way Eclair should have been.
The Android app store (Marketplace) has gotten some criticism, but I don't know how truly meaningful those criticism are, as I've gotten applications primarily based on recommendations, or searching the store with intent, rather than browsing the store. I recently had occasion to count the number of apps I have installed, and if you judge by Android's app management screen, it's now up to 70 (I have 93 icons in my app icon scroller view). I thought I'd list a few of the best ones, as a way of aggregating my own perspective from the different recommended lists I've seen. Some of these applications are not free, but as a developer I don't baulk at paying the small amounts charged, especially since returning for a refund is built into the marketplace if you don't like the app.
ES File Explorer is probably the single application that's most responsible for me preferring Android to iPhone. It's a file browser, but more than that: it can browse Windows (SMB) network shares, as well as FTP and Bluetooth. That means I can copy music, movies etc. on and off my device to and from my NAS. I find iTunes to be a tedious waste of memory and processes, not to mention it wants to update with huge downloads practically every second week, incorporating media players and web browsers I don't want. Crapware. Being able to take control of the media upload and download experience is wonderful, and makes me feel like my phone is more than a locked-down toy.
I complement it with Astro File Manager, which has better support for photo management and a built-in image viewer (which supports image view intents, so it can actually be used by ES File Explorer to view photos). I'm not a big fan of Nexus One's stock Gallery app (by CoolIris) - lots of gloss, but slow to index photos if you've taken a bunch. Astro can also act as a file selection agent for other applications that browse for an image, such as image editors.
Another photo viewer is B&B Gallery. It was one of the first to support multi-touch, manually implemented before the OS got support. An advantage it has over the built-in Gallery is that it doesn't downsample loaded photos, so you can zoom in and check the details, rather than quickly getting lost in blur. As a gallery app, however, it's not particularly pretty. I find file management superior, especially as you don't have to wait as thumbnails from all over the place get loaded, but can classify into directories, etc.
Act 1 Video Player is an excellent replacement for the stock video player. It doesn't add any more decoding capabilities, but it has better affordances in its UI, especially with its touch-based seeking support. Best feature: swiping left and right in the center of the screen seeks back and forth through the video.
NewsRob is an offline RSS reader that synchronizes with Google Reader. It has configurable caching, so you can have it download images which are linked from the RSS (a problem with Google Reader's own offline version using Gears, ironically), up to caching the full web page associated with that RSS item. Excellent for public transport.
A major annoyance with the iPod Touch (and also the iPhone) for me was the auto-rotation. I almost never want to rotate the view, and it always ends up rotating when I'm lying down, or otherwise not in front of a computer. I was only able to solve this problem on the iPod Touch by jailbreaking it. Android has a setting for this, but for easier access to it I use the AutoRotate widget. This lets you put a 1x1 widget anywhere which toggles the auto-rotate setting on a tap.
Some games are useful for passing idle moments. Robo Defense is quite addictive tower defense with RPG-like elements; you earn what are essentially XP points, and can spend them on incremental upgrades, so there's a campaign-like aspect to the gameplay. Replica Island is a classic-style platformer which is particularly ergonomic on the Nexus One, using the scroll ball for directional control. As an aside, controls are one of the weakest elements of most iPhone games - it badly needs more physical buttons. And Nesoid, an NES emulator, is nice in principle, but a better control system is needed.
Artistic diversions: DoodleDroid is a finger-painting app with configurable brush dynamics, so with care, you can get some interesting impressionistic images out of it. Simpler, more like coloured markers than paint, is Draw!.
Of course, there are the bar code apps, like ShopSavvy, probably the most integrated when you have buying intent, though its local shop search isn't very localized, even when in London; ZXing Barcode Scanner, which runs more general web searches based on barcodes; Google Shopper and Google Goggles also do barcodes, but I feel they're weaker, and Goggles is mostly a gimmick (IMO).
Google Sky Map is pretty neat - the way it uses the accelerometer to overlay constellations etc. is probably the neatest augmented reality-style implementation I've seen, even though it doesn't overlay on a video image from the camera. Layar is the probably the canonical implementation, but I find it to be too gimmicky in practice, having to walk around like an idiot with a phone held out in front of you. At least with stars, you're normally standing still and looking into the sky.
Google Translate is another essential app. It's tantalizingly close to real-time speech to speech translation; as it is, you can speak into it and at a button press do text to speech on the translation, providing the speech recognition was good. My girlfriend tells me it can be overly literal for German, however.
Wifi Analyzer helped me get better channel placement on my home wifi access points. Really neat live view of signal strength for all the different APs in your area, even ones too faint to actually connect to.
Arity is a simple expression-based calculator which can graph simple non-parametric functions in two and three dimensions. By non-parametric, I mean you give it an expression using x, or x and y, and it plots the result of the expression as y, or z, in a 2D plane or 3D volume. You can't plot circles with it, for example.
ConnectBot is a SSH client, useful for remote administration when you're really stuck for connectivity. Doing anything serious on the command line without access to a keyboard is insanity, of course. When the job you're trying to do is simpler - a single command over SSH - ServerAssistant is a better approach.
If you're interested in programming your life, Locale can trigger events based on conditions. Conditions are one or more of location, time, orientation, calls by contacts and battery state. Settings include wallpaper, ringtone, screen brightness, wifi enabled or not, volume, bluetooth, but also actions published by third-party applications. For example, NewsRob can synchronize based on a Locale trigger. And if you've installed ASE, the Android Scripting Environment, you can run arbitrary scripts - bash, python, ruby, etc. - on a trigger. The sample scripts available for ASE include invoking text to speech to say the time and the current weather, toggling airplane mode, showing notifications, etc. Locale is a lot less useful if you have a more flexible schedule, but if you're tied in to a timetable, it makes a lot of sense.
Finally, a battery widget: Battery Left. I don't use task managers or killers; I've found that it's better to let Android do its thing and kill what it needs to kill, when it chooses to do it. I get about 46 hours on average battery, but I tend to recharge before 36 hours have gone past. You can drop this widget as a 1x1 (or 2x1) visual indicator of battery left, with configurable detailed textual data: estimated time before battery dead, estimated time of day of dead battery, estimated battery %, etc. It monitors battery performance, so it should straighten the curve that batteries self-report - I've often seen batteries say they have three-quarters battery for ages, and then run out the remainder quite suddenly, etc.
Obviously, I have many more applications installed than I've mentioned here, but they tend to be single-purpose location-based ones that have less general applicability, or ones I don't use as often and can't in good conscience recommend. But I can say that all of the above work pretty well for me, and it's notable that many of them would contravene Apple's developer policy, so for me at least, app availability for the iPhone isn't the killer advantage it's made out to be.