A desktop can decode 1080p h264 video while the Pandora can only handle 480p. Using that as an approximate metric, the Pandora is about one quarter as powerful as a modern desktop with a single core.
I would estimate something a lot less generous, and I think your comparison is skewed by the fact that desktops could do 1080p in software for quite a while now.
Let's say on average around 1/3rd the perf/MHz/core of a Sandy Bridge. So if you have an i5-2500K like I do, which turbos up to 3.7GHz, the single threaded performance will be over 10x faster than even the 1GHz Pandoras.
Of course the actual numbers will vary a lot depending on the code. If your code is very cache friendly and the instructions are all scheduled nicely it can do better.
I kind of feel like not a lot of people want to give a very straight answer, so I'll make some random remarks that I think address the OP's question:
- The original 600MHz Pandora is about as powerful as a phone from mid-2009
- The newer 1GHz Pandora is about as powerful as a phone from mid-2010
- The original 600MHz Pandora can usually overclock to 900+MHz, but it's not quite as fast as the new one at 900MHz
- The newer 1GHz Pandora can usually overclock to 1.1-1.2GHz, making it still around the level of a 2010 phone
- Pandora has only one CPU core, which means that well-threaded software will show a bigger advantage on newer mobile hardware that has 2-4 cores. How much this matters varies a lot depending on the software - most emulators, for instance, are not that well threaded, but some are..
- The GPU on the original Pandora is really, really slow by today's standards. Mobile GPU power has increased a lot since then, a lot more than mobile CPU power has.
- The GPU on the newer Pandora is nearly twice as fast as the original's, but even then still very slow by today's standards.
- Software running on Pandora has some performance advantages vs software on Android and iOS thanks to some software advantages - like the ability to update to the screen very quickly, and some OS/driver tweaks. So it can often outperform similarly specced devices. It also helps that developers can optimize specifically for it. For example, even though I developed DraStic and gpu_neon with the intention of being useful on a lot of ARM platforms they're still relatively optimized for Cortex-A8 in particular so they'll run as well as possible on Pandora. Most Android and even iOS software isn't going to be optimized for any particular device or even CPU type.
- Compared to the other most developer/community friendly gaming handhelds out there, like Caanoo, Dingoo, or even GCW Zero Pandora is substantially
more powerful. You can get a more powerful gaming handheld/tablet from China (that'll also be a lot cheaper) but the support and community, and reliability for that matter, are not really on the same level..
- CPU-wise, the single threaded power of the 1GHz version is roughly comparable to PSVita, while the multi-thread power is way behind. But at the same time it's far ahead of 3DS, single or multi-threaded.