There shouldn't be much of an expectation from hardware like this; PS2 games typically output in 480p at best, and there's not much you can do about it. The only way to upscale the internal resolution is with emulation via PCSX2 or an old 80gb PS3, but that's not what I'm here to write about.
This device certainly outputs in 720p, but it "upscales" the image by softening it similar to the way Anti-Aliasing works. As such, nothing looks sharp or defined at all. Even higher resolution games like Gran Turismo 4 look blurry. I am also getting what appears to be a scan line on my screen; there is a faint horizontal line that stretches across the screen and slowly travels upwards.
It's worth mentioning that the sound is much louder and seemingly higher quality through HDMI vs component; however, this benefit is hampered by the fact that the video doesn't look much (if any) better than you would get from a ~$10 component cable. Your mileage may vary; perhaps I don't have the best TV for this device.
UPDATE: I brought this review down from 2 stars to 1 after a few days of trying to get along with this device. This thing is absolute junk. PS1 games have over-scan issues and do not fit on the screen. I can fix this on my TV, but then PS2 games do not take up the full frame. Additionally, a blue tint washed over my screen after a few hours of intermittent use. Straightening the cable going from this unit to the PS2 fixed this, but it's a testament to the shoddy build quality of these things if the angle of the built-in wire can cause some colors to drop out.
Pros: -Improved audio levels and quality -Doesn't stick several inches out of the back of your PS2
Cons: -Soft/Blurry image -Horizontal line on screen -Overscan issues with PS1 games -Overall typical cheap Chinese build quality -Cost compared to similar products of the same quality