My main problem I have with people is things either have to be a 0 or 10. I would rate it about a 7 myself mainly missing points for a bad menu system, some key games not having a patch to work, and some compatible PSOne games not working. I think 8/10 of my library works on it.
I think in my case the frustration stems from spending frankly most of my PS4 gaming time playing via remote play on Vita and expecting the same or better experience with the added Ethernet jack. I'm still not sure what the problem is but with everything wireless within arms reach there is still something not working as well as the famously bad Vita wifi chip. Wired seems to help with dropouts but not much for latency. I would just assume I'm crazy, but it seems to be a pretty common issue.
Maybe like is the case with framerate some of it has to do with being on a larger display and being more noticable but I'm not convinced. And this is all been used on a high end PC gaming specific high-response monitor. I don't dare hook it up to my normal TV at this point if I want to convince myself not to ship it back.
The only thing I can guess could be the issue, like others have suggested is something to do with converting the signal to 720/1080i within the PSTV. Perhaps because of cheap upscaling hardware there is a decent amount of lag introduced in the process? For fun I wired them through a gigabit switch in the same room with no measurable difference so thats all I've got left.
I have always found remote play to be good enough on Vita, but pretty close to the fine line. PSTV crosses into being something you notice the whole time and compensate for in a way that just isn't fun while playing.
I realize people have different tolerances for this kind of thing and for many it will be fine. But I have been left annoyed. The apps would have been great but I expected Sony to drop the ball on them. And compatibility isn't great, but ditto. The one thing I never expected was some bizarre regression in the one feature I figured would no doubt be at least on par with my Vita.
And to answer an earlier post, I'm pretty sure the PSTV connects the controllers via bluetooth even when they are plugged in and charging. Other than sending a quick authorization so that you can sync them. Having them use another protocol and direct connect would require extra firmware mods and maybe even hardware that wasn't onboard the Vita and I'm sure as hell sure Sony wouldn't invest in that when they can just beam it all over the existing connection and treat it like a dump-charging port.