I will chime in here, as someone who has tried to play and enjoy CO 3 times since 2009 (or maybe 4), and have not been able to get past level 22 because I get bored of it after a while... And who got multiple PCs to 50 in COH over the years.
Paragon City feels like a real place. People talked when the game finally went live again after all these years about feeling like they had "come home." (There is a reason this place is called "Homecoming.") The zones felt like regions of a real city. The NPCs had real personality. Contacts would snark you sometimes, or tease you sometimes (in the text). The factions of different good and bad guys like Skulls and Trolls and Council and Freakshows felt like they were real characters. And the city felt this way right from the first day I ever played it.
Millennium City and the other environs of CO don't feel like real places. They feel like video game theme-parks. The NPCs are shallow and wooden. They don't tease you or snark you (at least not in the first few zones, that I have noticed). The villain factions are unremarkable and I honestly can't even remember what they are right now, even though I last played it a couple weeks ago.
I also prefer both the sound FX and the music for COH vs. CO, but clearly that is pure taste, and even more subjective than my above statements, which are also, of course, subjective.
Aside from that, the biggest thing I prefer in COH vs. CO is just the UI and the control system. I find the COH UI to be pleasant, intuitive, graceful, and easy to use. I find the CO UI to be clunky, awkward, ugly, and difficult to use. And the control system in CO with the blocking (hate it) and the charge-up of powers (hate it more), is just not for me. All of the "old school" things that a few people have criticized about COH? Those are my favorite features of the game.
I feel like COH hit the market before a lot of the modern-style innovations of MMOs (most of which were derived from WOW, I guess) became saturated through the market. Nearly all MMOs play the same way now, and COH was built before that became entrenched. By the time the modern style had proliferated it was way too late to change COH to work that way (with things like blocks and charge-ups and combo moves and such). Since I prefer the old MMO gameplay to the current/modern style, this means the COH style suits me.
And then there are some of the innovations that COH invented and that, sadly, almost no one (or perhaps literally no one) ever copied, like the scaled (to team and level) instanced private missions (with difficulty sliders!)... or the Sidekick concept that allowed all of you to play together regardless of level. Does anyone do this today but COH? Does CO?
But then, as a friend of mine says, I took the Nostalgia pool power and I have it 6-slotted and perma'ed so... it's not a surprise that I'd feel this way.