I would say that text on the new iPad is actually sharper now, and font rendering is better than the Kindle.
One of the biggest advantages that E-Ink had over LCDs, other than being great to read in sunlight, was that there was no pixel grid on the screen. The new iPad doesn't have that problem either.
The screen on the new iPad can go dimmer than the iPad 2 (which already went dimmer than the original iPad) which makes it more comfortable to read in the dark than it was before.
The iPad is a considerably faster device as well. Even page turning is slow on a Kindle. (personally, I need to have it refresh every page, because it loses too much contrast otherwise)
The iPad doesn't need a light source to read books, whereas the Kindle needs quite a lot of lightfar more than a paper book or magazine.
The iPad is significantly better for anything other than plain text books, be it PDFs, illustrations, colour etc.
But I'm still keeping my Kindle. While it needs a lot of light, it's still perfectly readable in bright sunlight, or other situations where the iPad is unreadable due to reflections & glare.
The iPad Kindle app doesn't really offer any font customisation, and
still uses
justified text without hypenation, which leads to huge gaps between words and "
rivers" in the text. (the Kindle does this by default too, but it can be changed via the "Kindle Collections" plugin for Calibre) I don't have any problem reading on the new LCD (at least when there is some light in the room) but can't stand reading text presented in this manner.
Contrast ratio and viewing angles still suck on LCD panels. While it might be a nice thought to be able to use a dim sepia display, or white text on black, in the dark there are very noticeable shifts in contrast across the display when held at an angle, which I find distracting when reading a book.
The iPad is a much bigger and heavier device. While I find the new iPad to be better balanced than the iPad 2, I still don't like holding it for long periods of time when reading books. (the size may be an advantage to some though)
The battery life is terrible on the iPad, at least when compared to the Kindle. With an iPad you're going to get 10 hours, or maybe a little more if you're at a low brightness and get lucky. The Kindle will last a week or two on a single charge.
The biggest thing for me though, is that the iPad is a much more capable, always-connected device. When I'm reading a book I can get email notifications, messages from friends, alerts for other tasks. I'm two taps away from the internet, from watching a video, from playing a game.
The Kindle is a single purpose device that only does reading. You aren't going to be bothered by emails, and you don't really have the option of doing anything
but reading on a Kindle.