I have a PSP 1000 and I used to use that for homebrew.
But I ended up hating the thing, since it was so damn heavy!
(And I never liked the buttons either. The D-pad was stupidly spaced too much, and the buttons felt odd sometimes, and I LOATHED the thumbstick. That thing just grated the skin so badly. But again, this was the original PSP, and I've never used a newer one, so its probably improved a bit)
It did most emulators pretty well though, but the fiddling around and updating custom firmware was also pretty irritating.
Oh, and the memory cards, they are expensive and non-standard.
Seriously, a 16gb Memory Stick Pro Duo is still like £30-35, vs A Micro-SD equivalent of £15 and a SD equivalent of £12.
Then again, this is just my experience. Its probably not as bad these days.
And the emulation itself on the PSP was very good. (much better than the DS's at least! XD)
The newer PSP models are lighter, and you can get one of these adapters to make your life much easier:
http://www.amazon.co.uk/Micro-SDHC-Memory-Stick-Adapter/dp/B003RUFL7M/ref=sr_1_24?ie=UTF8&qid=1312698251&sr=8-24
But I will say that I LOVE my Caanoo.
Its has a nice weight, the buttons are nice, the stick, though a little odd at first, is pretty good once you get used to it.
It plays everything pretty well, and the emulation has improved quite a lot since it was launched.
The only emulators I personally have issues with are Ohboy (not the emulator itself, but the interface. The scrolling is a bit slow for my taste), and DrPocketSnes, (on mine it seems to crash sometimes. But my Caanoo is one of the ones that won't overclock to 800, (I think some Caanoos have CPUs that are slightly better or worse than others)). However, Snes9X4C works with some titles that DrPocketSnes has issues with, and the both together, do a pretty good job.
However, the only slight complaints I got with it is that the shoulder buttons are very odd, the volume slider has a delay (its a very minor complaint though) since its handled via software, the touchscreen and G-sensor is oddly under-utilised still by homebrew.
And the media playback isn't so good. Fortunately this has been improved quite a bit via homebrew though. Mplayer and Ommpc are vital apps.
I think eventually this will improve a bit more, but its still a bit far off.
Well I had to get a new emulation console a while back since, my PSP broke, (well it still works, but it is in poor shape ever since my stupid brother knocked it into the toilet. The Screen is water damaged, the UMD slot doesn't work, the battery was fried, the memory cards are a little dodgy, the buttons were pretty bad anyway, and it became very unstable, (got hot and sometimes used to crash when it shouldn't have)).
And I didn't fancy having to do all of the homebrew process all over again, so I got something that works right out of the box.
In fact the main thing between the two that needs to be compared, emulation wise, is the PS1 emulation.
On the PSP it was suprisingly good. Since it was built into the firmware and could be hacked to play other PS1 games.
There are quite a few games that work on it that the Caanoo doesn't do, and at better speeds.
The Caanoo PS1 emulator is suprisingly decent, but its still a bit off from being brilliant.
The Other main advantage the PSP has, is well, the ability to play PSP games! XD
In the end I think its a matter of preference.
EDIT: And other thing I'd like to point out is that the PSP had a LOT of homebrew developers working on it back then, (not so much now, theres the occasional release, but most devs have moved on to something else), and the Caanoo, well, has not exactly lit the homebrew scene on fire. (Mainly due to it being similar to the Wiz, but not directly compatible, and the Pandora taking the spotlight (good luck getting one of those! XD))
That being said, the few dedicated homebrewers that have released stuff for the Caanoo have done an excellent job.