I liked the earliest days of the JLA, back when they hung out with Snapper Carr and the group felt more like a social club for super-heroes. I find they get a bit tiresome when they start to feel more self-important and official. I guess it's the same reason why I like the JLI so much.
I really like the '70s Justice League. Loved the early stuff when Dinah was brought over and Ollie had his soft-reboot (lost the company that had never been mentioned before). I absolutely love those two pre-crisis (well, depending on the writer).
Atom riding arrows. I actually liked it best when Batman and Superman weren't as involved. Hawkwoman joined later, and that was good. I'm actually a big fan of early Ralph Dibny (with Sue), but don't really think he's suited to JLA. In one story he complains about the lack of good mysteries, and I agree. The League is more about fighting threats than solving mysteries to me.
As someone else mentioned, I like a Batman that's less grim. Bronze age Batman is a good balance, having depth and characterization and some angst without being depressing or too authoritarian. And he trusted his allies, which was great. He had faith in them.
I like the JLA as a loose association with no rank structure and limited rules (that "no duplication of powers" thing doesn't work for me). They share information and fight threats together. People in the JLA have their own lives and jobs and maybe even titles. I think works nicely as a contrast to the 80s Titans who have a clear leader and all live in one city and don't have their own books.
Dislike the idea of Snapper Carr. He should either be a member (he's come through several times) or not be present. Him as a sort of mascot or hanger on just grates on me.
Saw O'Neil mentioned earlier - I think he does some really great stuff. And some really bad stuff. Too many "issues" stories. I mostly agree him with on the issues. But the story needs to come first. Entertainment should be the primary objective, with moral messages woven in so well so you don't realize they are there at first glance. In the 60s, 70s, 80s ,90s, and still today you have some issues that are more like after-school specials. Not a good thing. Because they are extremely boring. I guess you have to consider the audience, though. I liked Captain Planet as kid - don't think I could stand it now.
Something else I liked about the Golden, Silver and Bronze eras of JLA was the 'villain of the month' format.
Aside from some two or three parters (mostly the annual JSA crossovers), the JLA went through villains at a pretty brisk pace.
It really filled up their world fast.
"There's magic in the sound of analog audio." - CNET.
I really like the first half of the bronze-era JLA. Decided to re-read over the weekend, and I kinda recall why I haven't read as much of the later stuff. The Conway stories just aren't as interesting to me. I'm on #161 right now, and for a good number of issues since Conway started writing, I've just read the first third of the story, then skipped to next issue because it wasn't grabbing me. Maybe if I take a break, I'll come back refreshed and more interested.
Steve Englehart's run was definitely a hard act to follow and I remember being bored to tears with Conway's first issues (#151-160). But #161 where you're at perked up with the addition of Zatanna. Maybe take a break, but definitely come back. Conway did a decent job with the book from #161-200 IMO. It wasn't Englehart great, but it was interesting enough.
I'm curious, how do like Dick Dillin's art? He was definitely a favorite of mine.
Did go back. It did get better, but not as good as earlier stories (even pre-Englehart) to me. I really liked the first part of Zatanna's storyline where she learns her memories have been altered. First issue with that story was good (well, her storyline). Unfortunately, I found the actual resolution and story that followed a disappointment.
The art - I liked it in general, but I'm not a huge art person. Unless the art is terrible, I usually don't really notice it until a third or fourth read-through, when I actually start to pay more attention. The first couple times, I'm usually too interested in seeing "what happens next" to stop and pay attention to the details.