What made vanilla epic to me all boiled down to a couple of important things.
-It was truly a social game. To be honest, I 100% believe that your success in vanilla was way more tied to your ability to make connections with other players on your server. I knew MANY absolutely terrible players that had a great reputation on the server, and therefore had no trouble landing groups and just having an overall good gaming experience. It was awesome knowing a huge majority of the playerbase. Passing by someone on a path, facing them in a bg, grouping with them, seeing their dead body outside of blackrock mountain, 9 times out of 10 you actually knew something about that player whether they were your faction or the opposing faction. Alliances and rivalries sprung up all over the place which added an awesome dynamic that I have yet to experience since.
-You WERE your character. I think this had a lot to do with me being a teenager at the time, and the fact that I had never experienced anything like WoW before, but every level, every piece of gear, every accomplishment wasn't simply increasing your character power it felt like a true accomplishment. Even before max level you felt like you were accomplishing meaningful things. I still remember small things like hitting lvl 30 and being so excited running back to my trainer to pick up the long awaited aspect of the cheetah. I had alts and such but i didn't think of my "main" as simply a character on my account, the character more or less was my account. For all the following expansions my "account" consisted of a roster of alts and i never really felt invested in a character again after TBC.
-The world felt massive and immersive. Self explanatory, when you had to run everywhere to get things done, you felt the scale of it all, and not being able to fly over everything, you were much more immersed in the world you play in.
-The playerbase didn't know every little detail about the game. There weren't as many resources to find things out about the game as there are today, and most of the playerbase wasn't too concerned about min-maxing every aspect of their gameplay. You could actually be "that guy" who does "that thing" that most people don't know about or don't pay attention to. On my server for a long time there was only 1 guy on alliance that farmed and sold savory deviate delights, only a couple who farmed winterfall fire water, most people didn't know where things like whipper root tubers or librams came from. Lots didn't know about the fishing contest or the STV arena, and the list just goes on and on.
-last one for me, all levels of content remained relevant. All the way up to when naxx was released, all other forms of end game were still relevant. You could be gearing up in dungeons or MC, or you could be in BWL all the way up to NAXX and you could find a guild that was currently progressing in any one of them. From like Wrath on that went away and only the very last tier of content seemed to be relevant and all other content was just "old"
Sorry super long post, bored at work