I've had a Kindle 1 for about eight months and a Kindle 2 for about two days, but already I can tell you that Kindle 2 wins this match-up, as least as far as I am concerned.
Kindle 1 is better because—
SD Card: You can buy a 4-GB SD card for it. This means you can swap out cards if you actually fill one up. Since now Amazon has arbitrarily removed books from people's Kindles (after refunding the price) because the publishers changed their minds, this might be more important than one would think. The weird part about this Orwellian behavior is, the books were 1984 and Brave New World, by George Orwell!
Battery: Even though the Kindle 2 battery lasts longer per charge, there is the little matter of not being able to replace the batteries yourself (I wonder if that's what the kiosk-like buildings Amazon has patented are for, or partly for? Kindle repair and service?). In the Kindle 1, you can pop off the back and change the battery yourself.
Booksmarks: Setting a bookmark is more intuitive and easier in a K1. Scroll to the top of the screen and press down on the scroll wheel. Boom! Done! It's not exactly tedious with the K2, but like almost everything else, you do it through the menu.
Wireless control: On a K1, you can look at the back of the Kindle any time and see if the wireless is on, On a K2, you have to take it out of sleep mode to see what shows on the screen indicator. Since the wireless sucks down the battery like nobody's business, this is annoying.
Kindle 2 is better because—
Speed! Almost everything (except bookmarks) is faster on a K2. The page turning is only slightly faster (it was pretty good before), but annotating a text is a lot faster, as is looking up words in the dictionary.
Searchable notes: This is a fantastic feature! Kindle owners have been asking from Day 1 for labels or tags as a way to organize their books, and this change (on the K1, notes you made in books were not searchable) means that you can now tag your books. The trick is to come up with tags that aren't real words so that they occur only in the labels you apply, like mistery, syfy, phantasy, readit, notread, etc.
Text-to-speech: This may not be that big a deal to some folks, especially since some publishers have turned this feature off, but as a writer I love it. I can send my own manuscripts to the K2 and have it read them to me! That's a great way to proof, because the K2 doesn't fill in missing words, or skip over excess ones, like my brain does. I still have to proof for misspellings but this helps a lot.
It's a tie:
The keyboard is a wash. The K1 keys are easier to press but the K2 has a more logical arrangement.
Likewise the case is more secure in the K2, since the Kindle clips into it, but on the other hand there are stories of folks whose Kindles' cases cracked from the new clips.
So now we're a two Kindle family. I told my husband I would try the K2 and let him know which one he was getting. Well, sweetie, congratulations! It's a Kindle 1!