This is one of those things where I don't feel like I can give a single definite answer. There's some openings where I prefer the music, some openings where I prefer the visuals, and some I don't like either.
TOS: I suppose the Courage fanfare and the opening narration are iconic, but I don't like the TOS theme music at all. It always felt very dated to me.
TNG: I love the camera panning out past the planets and Picard's update of Kirk's opening narration, but the rest of it is a bit... meh. The TMP/TNG title theme has become I suppose THE Star Trek franchise theme, but the TNG version always struck me as a bit pompous and high school band-ish, like it's being played slightly out of time and slightly too fast. Which is odd because I've loved the versions used on the movie soundtracks, and the one they sneaked in at the end of the final episode of PIC S3 moved me to tears.
DS9: Beautiful and haunting, with that magnificent brass melody... I buy the isolation, I buy the optimism, I buy the fresh new start, I buy the whole "we're doing the best we can with what we've got out here on the frontier"-ness of it all. Then the buggers went and ruined it completely in season four. Okay, I like that they made the station look busy and added the Defiant, the visuals were a definite step up, but who thought adding a Chariots of Fire bass line was a good idea!?
VOY: A visual tour de force given that this was mid-90s CGI, and Voyager's theme is fine, though I prefer the original version of the DS9 theme. Really there's nothing here I dislike.
ENT: Visually brilliant; possibly my single favourite Star Trek intro. Musically an abomination. And then somehow they made it worse.
DIS: It looks and sounds a bit like it's trying to be Star Trek: Fringe. I don't like the theme music at all because it's unhummable ambient pish, and why is the title sequence beige? I do quite like the way ship emerges from its own technical diagrams though.
PIC: Didn't mind the first season version (music and visuals), hated the second season version (music and visuals), but the third season version showed us what everyone knew all along – that they should have just used the First Contact theme from the beginning. Also, love the LCARS visuals in the third season. Though I suppose they're technically closings rather than openings. Why didn't they just put it at the beginning? Weird.
LDS: The music is fine, but I find the title sequence a bit too long and self-consciously funny and I often skip it. I like the running joke of the Cerritos stumbling across a bigger and bigger battle every season and just noping the hell out of there though.
PRO: This is kind of the DIS title sequence done right. Exciting theme music and visuals including all the characters and showing off the ship. I like it. I'm very intrigued to see how they update it for season two.
SNW: Well, I mean, it's basically hardcore starship porn isn't it. Absolute filth! Also, even though I don't like the TOS theme music I like the way they did callbacks to it here. It's like it's building to the TOS theme, just as SNW is narratively building towards TOS. I like it a lot.
So to my surprise it looks as though the openings I like most are VOY, PRO, and SNW. I seem to have issues with all the others in some shape or form.