I didnāt answer because Iām not sure I have a favorite. I like (and dislike) each mission for different reasons.
Algorithm: ISICās dialogue is amazing and the progress through Fort Ocoban has a nice cinematic feel to it. However, Ronin are the devilās children and the final phase of the ISIC fight is a bitch and a half if youāre melee (ran it yesterday with a friend of mine; he played Boldur and I played Kelvin; we spent like 5 minutes jousting with ISICās head as he repeatedly juggled one of us and constantly kept out of melee range otherwise).
Voidās Edge: Thereās a Wolf Sentry in this one. Automatic win. But the mission feels like itās missing something, and Iām not sure what. Itās lacking that je ne sais quoi.
Renegade: So much stuff to kill and fun to fight but doesnāt really have the level of awesome dialogue that I come to expect from Gearbox (and is present in all of the other mission; they canāt all be amazing).
Archive: Wolf Sentry means awesome. Difficulty is right on target, but itās stingy with loot (only one boss and just a few 6 chests). Just like Voidās Edge, thereās something missing to really push it over the top.
Sentinel: I have run this an almost insane number of times so it has kind of gotten old to me. On the plus side, the chests are all in predictable places and itās got some of the best legendaries so itās a great dungeon for gear. On the negative side, the dialogue/story is kinda boring (at least, for me, now it is; I remember enjoying the story back when I hadnāt run it into oblivion because of Novaās monotone reading of the Sentinelās messages) and those damned golems are the most annoying enemies in game (theyāre immune to crits, including the bosses; have copious amounts of knockback so it sucks to be melee; they can only be hit from the front in the center of their chest but love to run at an angle so you canāt get to their chest unless you stun them).
Experiment: The dialogue is superb, but the difficulty is annoyingly high, not because of the enemies (though it does spawn Ronin /shakefist) since you have to guard the same location multiple times and it never gets healed (unlike Archive, where the Librarian gets healed during the minion phase). Itās also light on gear, in my experience (2 bosses and I can only ever find 1-2 6 chests), though it does have some nice drops from those bosses.
Saboteur: A lot like Experiment, the dialogue is amazing, but the mechanics of play make it less fun than it could be. It also feels light on loot.
Heliophage: On normal, itās a nice stroll through Tempest and the Void, smashing Thralls and Varelsi. The call backs to the previous content in the Void are fun, but it is woefully lacking on gear since Rendain is the only boss that drops gear and there aren only 2-3 6 chests. On advanced, it is a meat grinder of epic proportions; fighting 2 bosses simultaneously 3 times is rough, especially when there are massive elite Thrall spawns at multiple intervals throughout the fight. On advanced, when you beat it, you definitely feel like you earned it and, since itās the āfinalā mission of the game, the difficulty is appropriate, imo.
If I had to choose a favorite, Iād probably pick Archive. It doesnāt achieve the same highs as other missions, but it definitely avoids any of the lows (associated with fun, that is; lack of loot means I donāt run it as often).