I have and love the Axim... well, I have the x51v. If it were a choice between that and the TX, I would be very much in favor of the x51v, because of the VGA screen. Between the two lower res devices, I'd probably go for the Palm. But AFAIK, the surfing experience is much better on the Axims and on Windows Mobile than it is on Palms. The mail app is very nice, although nothing overly special....
Some things to be aware of:
1) Currently, there's nothing that will let WM5, the operating system the Axim uses, sync with a Mac. Neither of the two companies that make third party software have announced a promise date on releasing updates, and they've been working on it for several months... It'll come eventually, presumably, but it seems to be relatively complex.
2) WM5 also has compatibility issues with a lot of existing Windows Mobile software.
But all in all, I really do like my Axim. I love the fact that it has two card slots, so I can use my CF cards from my DSLR in it.

And Acrobat is gorgeous on the VGA screen.
I go to an Axim site...this may be a biased take, but... here is a thread there about the x51v and the TX...
http://www.aximsite.com/boards/showthread.php?t=109496&palm+tx