It's always interesting to see the variety of reactions/opinions that folks have on these things.
I do think that switching away from the PSP battery was probably the better decision. The battery I have is a 2000mAh one, while the original PSP battery is only 1200mAh. And I know that OtherMod is working on a variant that uses an extended battery, which he reported gives something upwards of 20+ hours of gameplay. And, like someone mentioned, the original PSP had some kind of special chip in the battery, which is why you needed a special battery to jailbreak it, if I remember correctly.
The CPU and memory on the Pi Zero is also much better than what was available on the original PSP -- 1Ghz/512Mb (Pi) vs 333Mhz/32Mb (PSP).
The replacement screen is the same resolution as the original screen. Yeah, it would have been nice to be able to reuse the original screen, but that wasn't a deal-breaker for me. Honestly, for about $110 US, I thought this was a rather affordable option for getting a handheld device that I can run Linux on and write my own games for. And it's a much better option than me trying to string together a bunch of random parts from Adafruit or something.
My biggest complaint with the device actually isn't the hardware itself... it's RetroPie/EmulationStation. It seems you always need to be switching between the main UI and some NCurses-based interface to configure some setting. I'd say that detracts a bit from the overall experience, compared to the original PSP firmware. Though I'm sure that situation will improve with time. Someone will write an alternate launcher, port one of the other ones, or improve ES.
Overall, I'm definitely enjoying the device. And as someone mentioned, even the experience of building the thing was definitely fun/worthwhile. Having done that, I now have much more appreciation for how much work went into designing a custom motherboard like that and making everything line up correctly. It's pretty cool.
[doublepost=1521859548,1521859067][/doublepost]Oh, and one more thing I forgot to mention. I also own the GCW Zero. Which is pretty comparable to the PSPi in terms of CPU and Memory (1Ghz/512Mb), but the screen on that is only 320x240. I think the big mistake with the GCW Zero was choosing such a low screen resolution. It's really not useable for anything but the oldest games, and the community around it seems to have died (at least if updates to their website / development toolchain / games are any indication). If the GCW Zero had a screen comparable to the PSP or even the Pandora, I think it probably would have had a longer life. So that was partly my motivation for buying both the PSPi and funding the Pyra -- I'm still in search of the perfect device...