Yes, component is good, and certainly better than composite. But no, it's not as good as HDMI, at least specifically in terms of PS2 vs PS3. I had the PS2 component cable back in the day. It only outputs at 480p. It was an obvious improvement when I got the PS3 and started playing my PS2 games there, even if it was only upscaled. It's a cleaner image. And that's even before talking about the convenience of having audio and video in one, being able to play all your games on one system, not having to buy converters, extra cables, etc.
My PC is hooked up to the same TV as my consoles, so unless Sony throws us a bone for BC, I'll probably stick to emulation (of my legally purchased PS2 games, of course).
Audio being separate is a pro for me, hdmi is a step backwards imo. Always trouble with it. My PC will only output stereo over HDMI, My receiver has no 4K pass through so I'm limited to ARC which is limited to lossy 5.1 instead of PCM (which admittedly is a limitation of toslink as well from ps2). Sometimes the sound randomly cuts out or the picture goes black for a second for no reason, or my amp and ps4 get into an endless handshaking cycle, no sound just blinking between formats. I've never had any of those issues with component video and digital audio. Of course component video tops out at 1080p and digital audio (AC3 or toslink) don't support linear PCM beyond 2.0
My ps2 looks great on my 4K tv (my phat ps3 died as well, no ps2 BC anymore) through component video. I hardly ever use it though, but my kids were going through Baldurs gate alliance and Champions of Norrath for a while, still looked gorgeous. We need sequals to those, split-screen co-op hack 'n slash is always fun.