well there are a *lot* of power joys out there.. they're still using the brand name today on various things.
the original (I guess?) would be the N64 controller/gun hybrid design, some of these (maybe all of the originals?) had 10 hacked games built in. the earlier version came with a 64 in 1 multicart of mostly standard Famicom games, later with an 84 in 1 (of which there seems to be a few variations). there were a few more variations with, I think, the same 84 game set, the Power Joy III, Voyager and Solo (maybe?).
after that they started releasing versions with Nice Code games bundled, like the Supermax (60+30 games), Navigator (50 games), Streamline and Mega Racer maybe?
after that point it seems like the Power Joy Ltd company in the UK that had been coordinating international efforts was shut down, and the brand was then used by Trump Grand (the original manufacturer in HK/China) on a whole range of cheap famiclones, which seem to have been mostly sold in the Middle East and China (if they were sold anywhere at all) and mostly reverted to including sets of pirate Famicom games rather than any original Nice Code stuff. and that's how it's continued to this day, with ever-diminishing build quality.
and as far as batteries go, I think all the ones in the "classic" N64+gun powerjoy design take AAA batteries, some others probably use AA, some use AC adapters..