Long time former FFXI veteran here. Played since NA launch in '03 and played for about 8 years. This was a game that was very tough starting out and was pretty unforgiving, but any time you finished something it felt like an accomplishment. First and foremost the game put a HUGE emphasis on teamwork. Unlike WoW where you just grind your way to max level then started doing raids, you needed to party pretty much just to level up. Also party dynamics were key. The basic formula was Tank, 2 DDs that can weapon skill chain with each other, a nuker (Black Mage usually), a healer, and a batter (Bards and Red Mages usually filled this role.) Obviously some jobs were more in demand then others (just like WoW, good luck finding a healer), but the thing I liked the most is you had all of your jobs tied to 1 character, instead of creating a million alts. Any race could be any class and you could switch between them at major cities or small towns.
This was a game that early on really put the emphasis on working together, as that would always result in killing faster, killing stronger mobs for more exp, and keeping a chain going so that you can multiply the exp the faster you can keep killing. As the game progressed however things started to become a bit more lenient in terms of teamwork as new mobs introduced through expansions started to come with specific strengths and weaknesses that were more exploitable (Colibri birds come to mind, where their weakness to piercing attacks put a premium on Dragoons, Rangers, Thieves, and polearm Samurai's, but their ability to mimic magic made them impossible for Black Mages and Scholars, but they had slimes which were physically resistant but were super weak to magic)
I think the real stories came from endgame though. Fights between Linkshells (Guild equivalent) getting claims on high end super strong monsters (Hello Fafnir and Nidhogg) or claim spots for Byakko and Kirin. The most legendary story however, had to be this 1 group who decided to take on Absolute Virtue, at the time the strongest opponent in the game to which nobody has ever defeated. Ever. Seriously this guy was a beast. Some shell on Odin decided to take him on (to fight him you have to already go through a fight with the Jailor of Love, another high end monster, and then Absolute Virtue was a random spawn after.) They decided to take him on, and fought him for 36 hours...straight...no breaks. They managed to drop him to about 40% until eventually they just ran out of gas. Still, however, this was something that was of legends (up until some japanese LS found out you can just kill him with a bunch of Dark Knights with Kraken Clubs using Souleater and Blood Weapon and burn him down in 90 seconds, to which Square enix quickly then patched so that AV had resistance to souleaters extra damage boost.)
Still, I loved FFXI a hell of a lot more than WoW. WoW was just boring and endless roaming, killing, rinse, repeat. You didn't have to talk to anybody. You didn't have to work out strategies until endgame (you can skip the alternative dungeons leveling up, so no point in doing them.) FFXI just felt like you knew everybody. Everyone eventually parties with people. You work out combos and order of weapon skills. You actually talked to people, and that's why I always loved FFXI. It was hands down my longest experience with any MMO.
(For the record I played WoW for about 2 years, Guild Wars 2 since launch although I haven't really been playing recently, and Wildstar for maybe 3 months...it was flavor of the month...I was also in FFXIV alpha and it was horrible, although I know they completely rebuilt it from the ground up and it's a lot better, but I just don't have the time anymore to play.)