I actually wasn't going to get a new iPad. Which should be called the iPad 3, but Apple didn't ask me. I liked my iPad 2 just fine. I sized up what I did use it for and decided a Kindle Fire would be a fine purchase: my dad wanted my Kindle 2nd gen, and my girlfriend was limping along with just an iPhone and a horrid Dell netbook. It looked like torture to watch her using it (to an Apple geek living in the first world: torture...can these problems BE any more high class?). I was looking for a used Macbook for her, but I hadn't found anything that could run Lion and wasn't as much as a new laptop, so I was considering giving her the iPad 2 and upgrading but hadn't committed to it. Fortuitously, I went to Wal-Mart at 12:30 AM the day the new iPad came out to get my Fire. I hadn't considered that 12:30 AM counted as launch day. I got my Fire and the electronics dude said he had two new iPads left. I bought one thinking I could sell it for extra on Craigslist and offset the cost of the Fire. When the iPad 2 came out, supply was so short I paid an extra $100 for mine. I felt smart and entrepreneurial. Well. Supply has been plentiful. So I gave the iPad 2 to my girlfriend and finally opened the new iPad. It's pretty. I wouldn't have bought it if I'd known I'd be keeping it, but since I have it I'll keep it, and the girlfriend is fine using the iPad 2 as her primary computer. You can do that now, what with iCloud and such, if your needs are less complicated than mine. That's pretty cool.
The screen is noteworthily better for text, but I still prefer reading on the Fire because the iPad is both heavy and sharp. It actually puts painful creases in my hands if I hold it and read for very long. It's WTF sharp. I ordered a case from Amazon that will cover the edges. I'm all about being on the cutting edge, but not literally. So, for reading Twitter, Facebook, and RSS feeds, the new iPad is excellent. It's absolutely gorgeous, and I've always preferred iPad apps for consumption. For long reading bouts, though, I'm a Fire fan. The screen is not e-ink, and it's not as good as the new iPad, but it's a barely perceptible difference to me. It's extremely comfortable to hold for long periods, too.
I haven't noticed any speed improvements. iPhoto still spends a crapton of time "rebuilding photo library." I don't have much affection for iPhoto. Snapseed still works better IMHO. But I digress. If I did a lot of graphics-intensive gaming, maybe speed would be more evident, but the most intensive stuff I do is photo processing, and that is still slower than I'd like.
I don't care about the cameras. I have an iPhone 4S that I use for almost all my photos. I guess it's nicer for FaceTime, but only if the other person also has a new iPad.
Best feature, though? The battery life is like CRAZY long. I don't know if it's the new Bluetooth technology or what, but there must be some crazed Energizer bunnies in this thing. It keeps going and going and going.
In summary, my opinion is what the consensus seems to be elsewhere: this is not a must-have upgrade, but if you have the money or end up with one somehow, there are distinct advantages to be had. But also buy a new case that goes around the edges.