I've only played on VITA and it is still a lot slower than PC.
Are we sure this game works for PSTV? From what I know not all PS1 games work on PSVita.
Toy Story 2 has a regular PSN release as a PSOne Classic, meaning that it can run on PS3, PSP, PS Vita, and PSTV when purchased through the PSN store. I can confirm that it runs on my Vita, however the input lag is beyond atrocious and is literally not playable even casually, let alone competitively in a speedrun setting. I could compare load times on my vita, which in theory should be the same as PSTV loads, but it's not worth the time because no one would be running the PS Vita/PSTV version anyways due to the input lag.
(And just as a side note, I'm not even joking when I say I think I get better response times literally streaming games from my desktop to my Vita with moonlight/nvidia gamestream over my local network vs playing the PSN version of Toy Story 2 on my Vita)
Except for me and Zic.