It's cheaper than the Sony, it has a bigger capacity and the books are cheaper to download - free in some cases. The 3G version also has wif-fi so that you download directly to it (with Sony, you have to download via a PC).
On the down side, the major library suppliers seem to be going with Sony, so if that's how you get most of your books, then perhaps the Kindle wouldn't be such a good idea.
The Sony one (or compatible ones) and their books are more widely available.
In general, an eBook reader will never be a proper substitute for a real, paper book, especially when it comes to children's books and those lovely picture books we all like to have around the house. But if you travel or have limited space for book storage, then you can have up to around 3500 books taking up less space and weight than a single paperback. Plus your 'books' will always remain in pristine condition and there's no danger of lending them out and not getting them back again.
I did actually roughly cost out that at an average £8 per paperback novel, I'd spend around £32 per month (£364 per year) if I bought them all new. At around half that or less for eBooks, and at around £150-£160 for the average eBook reader, it could pay for itsself in less than a couple of years, sooner if you read more than the three or four books per month I currently read.
It'll also save on a few trees.