To answer the original question, yes, PS1 games most likely lag more on PS3 than PS2 (although not always the case).
This is because PS1 games on PS3 are emulated fully through software, and PS1 games on PS2 are partially emulated but has the PS1 CPU built into the motherboard (used as an
I/O processor). The later models of the PS2 (slims) do not include a "dedicated" PS1 CPU. These models are generally worse at compatibility due to the IOP being emulated.
Now, if we're talking about loading backups through USB (PS2) or hard drive (PS3), then the PS3 is probably better than PS2. This is because the IOP in the PS2 will be fighting for bandwidth (pretty much everything is connected to the IOP). Not even mentioning the software limitation. POPStarter for the PS2 is based on the official PS1 emulator for PS2 (contains Sony copyrighted code), which is why it's very iffy to work with since it's a legal gray area.
tl;dr It depends on what media format you're using. PS2 fat is best with PS1 discs, PS3 is best for PS1 digital games.