Given the fact games like Dissidia 2 and Monster Hunter are coming out for normal PSP next year and TGS has so far not shown any new version, we probably not seeing it for a while. Maybe next holiday at the earliest.
I highly doubt the PSP2 will have 3D since they're pretty adamant about not putting it into handhelds, plus it'd be a conflict of interest to have a glasses free device when they're pushing with-glasses 3D, but who knows what'll happen in a year? At the very least, Nintendo will have a head start on this.
It will likely be more powerful than the 3DS graphically, though I wonder how far they'll go. Put the graphics too low, and the 3DS will seems so much better with the added 3D. Make the graphics too great and while the games will look amazing, they'll be a lot more expencive and take a longer time to develop for, which could really hurt the third-party support, especially since the PSP2 likely will not reach the same level of support the 3DS has. They really need to find a happy medium, and I'm not even sure if that'll be enough.
It'll probably be physical media/download. Sony was burned by the Go so download only is out, unless they really push it next iteration (unlikely).
It almost certainly will have dual analog. Thought this is Sony we're talking about, they could be short-sighted enough to not include it. Maybe touch screen as well, no idea what they'll do there.