I've had both. I like the Visor (Handspring) better, but don't really know why. The Visor line is cheaper (price wise), and when I bought, the complete Visor line came with a USB cradle, where as the Palms came with a Serial one. You can get the "other" cradle from either if you want to pay extra or wait for it.
The Handspring folks seem like they beat Palm to the punch more too. The next greatest device is usually by Handspring (ie: Handspring Trio), as appossed to Palm (Windoze CE is different).
But, keep in mind that the Handsprings run the actual Palm OS, so is Palm changes the OS, the Handspring is then behind till they rewrite it (or pay Palm for it).
Also, I haven't kept up, but Handspring was in the process of purchasing Palm. Maybe that tells you something about the situation.
Either way, if you do not have any "palm" device, you need one, and I think you would be very happy with a Handspring Visor, as I am.
Its like this (if you don't know). A Visor (Palm) is definetly something you DON'T need, but once you have and use one, you can't live without one. It is that cool...