2-3fps is weird. They should all do (lossy compressed) 1080p30 over USB 2.0.
The lowest end of HDMI captures used to use HDMI-PAL converter wired to an S-Video capture chip onboard. That was completely superseded by MacroSilicon MS21xx chips that actually capture HDMI. The ones that are now everywhere are based on those MacroSilicon chips.