IMO the only two competitors worth mentioning are the Samsung Galaxy Tab 10.1 and the Motorola Xoom. EDIT: Oh, and maybe the ASUS Eee Pad Transformer.
The Tab 10.1 costs the same as the iPad 2 (e.g. £479 for the 32GB WiFi-only model).
The Xoom used to cost the same as the iPad 2, but recently had its price slashed (allegedly due to poor sales) - it's now (IIRC) £400 for the 32GB WiFi-only model and £479 for the 32GB WiFi+3G model.
The Tab 10.1, the Xoom, and the Eee Pad all use the Tegra 2 System-on-a-Chip (SoC). This has an ARM Cortex-A9 dual-core CPU and a GeForce ULP GPU. All three have 1GB of RAM.
The iPad 2 uses the Apple A5 SoC. This also has an ARM Cortex-A9 dual-core CPU, but has a superior GPU to the Tegra 2 - a PowerVR SGX543MP2 dual-core GPU. However, despite having a superior GPU, the iPad 2 has less RAM than the Tab 10.1 / Xoom / Eee Pad - 512MB rather than 1GB.
Of the Android tablets, I believe that the Tab 10.1 has had better reviews than the Xoom originally had.
Do you have a smartphone? If so, do you have an iPhone or an Android phone? If you already have an iPhone, that would make choosing the iPad 2 easier, and if you have an Android phone (e.g. Galaxy S etc.), that would make choosing an Android tablet easier. e.g. As I have an iPhone 4 and an iPad 2, I don't have to worry about having two different OS's to get used to or to download apps for - apps I already had for my iPhone 4 will also work on my iPad 2, whereas if I'd bought an Android tablet, I would have had to start up a separate app collection for that.
The iPad 2 wins when it comes to apps. It's also ridiculously easy to use, with an intuitive UI.
Android tablets win when it comes to customisation, and additional interfaces such as USB, HDMI, SD cards (if you want these for the iPad 2 you need to buy add-ons). I haven't used Android, but Honeycomb (the tablet version) is meant to be very good (although I think reviews of the initial release, at least, mentioned buggy-ness...). Do you really need a tablet with an SD slot, HDMI port, etc., or does it not really matter to you?
There is also Flash... the iPad 2 (and all other iOS devices) cannot run Flash. However... so what? I try and avoid Flash whenever possible anyway on my Win7 PC, and don't miss it at all on the iPad 2. The iPad 2 does not need Flash for the BBC iPlayer, or 4oD, or the ITV Player (all have apps) - EDIT - there's also a Demand Five app due later this year; the iPad 2 does not need Flash for YouTube (there's an app, plus it works via the browser); the iPad 2 does not need Flash to stream Freeview channels for free via
TVCatchUp.com (works via the browser). What other uses are there for Flash? Adverts? I don't want to see those... Browser games? I don't play those anyway. Websites? I think websites built in Flash are an abomination.
Do you have an Apple Store nearby? If so, pop in and have a play with one of the display models, or try PC World / Currys etc. and play with theirs. Have a play with a Tab 10.1 etc. too if you can (PC World / Currys should have them on display I think).
AnandTech - iPad 2 preview & benchmarks
AnandTech - iPad 2 GPU benchmarks
AnandTech - iPad 2 review
AnandTech - Xoom review
AnandTech - Galaxy Tab 10.1 review
EDIT:
AnandTech - ASUS Eee Pad Transformer review