Simple question: Do you want a tablet device?
If the answer is yes, then the next question is "Do you submit your computing choices to a Purity Test?"
If the answer is yes, then maybe you go look at the Xoom. You probably don't get it, though. Any other answer - you get an iPad 2. Period. Because the iPad 2's added features (double the CPU power, double the RAM, lighter weight) pretty much are there to match/trump what everyone else just tried to come out with this year.
Sure, 7-inch tablets are smaller and lighter. They can't match the battery life of iPad (or the other 10-inch devices) but they arguably fit in a coat pocket. Apple's not playing in that space, so if you want a 7" tablet you can't go Apple.
The Xoom is the only mildly competitive device in the iPad's class that's shipping (HP and RIM aren't even on shelves), and even then it's pretty clearly still a work in progress. There aren't really any 10" optimized Android apps that play nice on Honeycomb yet, there's no easy direct desktop sync (Google services are the way to go), the 4G upgrade, when it's ready, will require you to mail it out for a week or so, the SDXC slot doesn't work yet, and Flash is still pretty much a pipe dream. Inhatko nailed it when he said that the Xoom, while nice, looks like it was designed by angry Soviet prison labor next to the iPad.
Now, as for what the differences mean - I owned an original iPad. It was one of those devices where you almost couldn't explain it - you had to hold it and just try to use it for something, then you got it intuitively. After I started using it, my laptop became a desktop, tethered to a big screen and keyboard when I was in the house. I almost completely stopped using it in any other room, because the iPad filled that need entirely. Sure, web pages could be a little slow to load compared to a desktop. Yeah, things take a while to boot. But hey, Angry Birds!
The iPad 2 has made that go away. First of all, iOS 4.x's multitasking abilities allow easy switching between apps. The extra 256MB of RAM (now 512MB total) make sure that most apps don't get swapped out to reload fully, and web pages rarely need to refresh. Having 2x the CPU helps as well - rendering is desktop-fast, while games, apps, and the UI are instantly responsive. There's no real difference under the hood otherwise except for the addition of a gyro chip which will mainly impact gaming. The resolution is the same 1024x768 - the GPU though is rated at up to 7x the speed of the last version, and from playing a few games on it I can see the difference even more starkly than the raw CPU power indicates. There's plenty of framerate and rendering benchmarks published so far.
Battery life is still the same - a class-leading approximate 10 hours. Still the same buttons, no extra cruft added on. The same peripherals work as before, minus the Keyboard Dock (which wasn't that popular - a regular Bluetooth keyboard will still work fine if you like). New this year is a HDMI cable with a sync-charge passthrough, it supports display mirroring and presentation mode (mirroring only works with the new iPad - the old one will allow presentations). The missing 4 ounces aren't noticed too much - the thinness, very much so. Even with the Smart Cover it's thinner than the original iPad. The feel is much closer to a unitasker like the Kindle now.
[Edit: added paragraph below 3/15]
As for the much-ballyhooed cameras, yes, the iPad now has front and back cameras in order to use FaceTime (now a standard part of the Mac OS as well, and it'll push away iChat AV over time). The front one is a pedestrian VGA resolution, optimized for video chat and not much else. Serviceable but nothing special - the same as the camera on its iPhone cousin. The rear camera is only equivalent to the camera chip in the iPod Touch - it's optimized for 720p video and takes slightly lower-res still photos. Why doesn't Apple put a better chip in there? I don't know for sure. I think part of it is the thinness of the iPad 2 - it's actually thinner than the iPhone and there may not even be room for a better imager. My main suspicion is that Apple simply decided that you may show/capture video with the iPad but anybody really thinking about still photography with a 10" tablet probably should either get an iPhone or carry a real camera. Even though video chat has become a checklist feature nowadays, I don't even think it'll be as big on iPad 2 as it is on the iPhone - with the higher weight of a tablet, people who use it for chat will need to make sure they keep their nose hair well-groomed!
In the end, the iPad 2 isn't a revolutionary improvement. It's evolutionary, and that's fine. It more than keeps pace with the rest of the market, and given the lead Apple started with I don't see how that's going to change at all this year. When you sell 15 million iPads in 9 months you don't have to reinvent it the following year. The burden is on the rest of the market to catch up. Things like the Smart Covers (held in place with hidden magnets), the GarageBand app, and the latest iMovie? Well, that's just piling on. Apple will likely sell more Smart Covers this year than the completion will sell tablets, combined.