Not really anything there they couldn't do with a redesign of the current model. Why bother with a whole new platform if all you're going to do is a "slight" jump in graphics, unless you've got some other major innovation to make up for it? (a la the DS).
I imagine the PSP2 will come out towards the end of the PS3's life, and will have graphics comparable to it. That won't even be very hard to do, since it'll only have to push a fraction of the screen resolution (increasing the res of the handheld's screen doesn't have to be a priority). What other innovations they might include I'd rather not guess.
Since the uncapping of the processor, I think the PSP has pretty definitively surpassed the PS2. Compare the cutscenes of God of War: Chains of Olympus to GoW2, for instance -- the PSP is miles ahead.
Edit: missed this:
Highly arguable. That approach apparently results in more popular games, but I've seen little evidence that they're better. As it happens, even though I love the idea of the DS, there isn't a single title on it I'm interested in owning. Getting more popular, better-selling games will obviously be Sony's primary concern with its next handheld, but it may recognize that it can't compete with Nintendo on Nintendo's terms. In that case, it may try to continue filling the core gamer niche that Nintendo will likely again leave wide open. The PSP hasn't done all that shabbily on that path, after all, and most of its failures come from things that can be corrected without changing this basic strategy.







