I own both of these readers, and I love them both. I think you'd be happy with either one, but here's my opinion (take it for what it's worth!)
Sony: It's lighter and has physical page turn buttons, which I actually like. It has more dictionaries, which I haven't used, but the coolest thing is that when you highlight a word to look up, you also have the option to use google or wikipedia. I've come across a few words which weren't defined by the chosen dictionary, and it was truly handy to google the word.
Borrowing from the library directly from the reader is a breeze, although it takes patience. It's not particularly fast in its web browsing, but it does alleviate the need for a computer. That being said, I normally just download the borrowed book via my PC and transfer it to the reader.
I also like how when the reader is in standby, you see an image of the book you are reading instead of an ad-based screen from Amazon. But this truly is a minor detail, because I've actually used a few of the 'special offers' from Amazon. The Sony reads epub and not mobi, but this isn't an issue for those of us who use Calibre and can convert easily.
The Sony is reflective, but when in a cover it's not that terrible. The kindle clearly wins here, in my opinion, as there is no reflection at all from the kindle. However, I love the red color of my Sony and color choice is always good.
Kindle: It's heavier but as far as touch-screen page turns, I find it to be quite easy to use. I'm not one of the ones who seem to have issues with a too-sensitive screen. It's tied to the Amazon kindle store so when you purchase a book, it uses whispernet to wirelessly download the book automatically (next time the kindle is powered on.) The special offers are at times very good deals, I've gotten a few 99¢ books this way, and a discount on a cover. Putting the books into collections is quite the ordeal and I have yet to find an easy, efficient way to do it. And if you don't do it, you'll end up with pages upon pages to scroll through on your home screen.
As far as reading, they are both really great. The font selection on the Sony is quite a bit better, but I can easily find a font I like on the kindle.
I have found that Amazon usually always has better pricing on books. And always tons of free books.
I hope this has been helpful to you. My decision to keep both really came down to the fact that I really do love both of them, and I've justified it to myself (logic notwithstanding) that although I can convert mobi to epub and back all day, wouldn't it be
IDEAL to have a reader that reads both formats?