I didn’t answer because I’m not sure I have a favorite. I like (and dislike) each mission for different reasons.
Algorithm: ISIC’s dialogue is amazing and the progress through Fort Ocoban has a nice cinematic feel to it. However, Ronin are the devil’s children and the final phase of the ISIC fight is a bitch and a half if you’re melee (ran it yesterday with a friend of mine; he played Boldur and I played Kelvin; we spent like 5 minutes jousting with ISIC’s head as he repeatedly juggled one of us and constantly kept out of melee range otherwise).
Void’s Edge: There’s a Wolf Sentry in this one. Automatic win. But the mission feels like it’s missing something, and I’m not sure what. It’s lacking that je ne sais quoi.
Renegade: So much stuff to kill and fun to fight but doesn’t really have the level of awesome dialogue that I come to expect from Gearbox (and is present in all of the other mission; they can’t all be amazing).
Archive: Wolf Sentry means awesome. Difficulty is right on target, but it’s stingy with loot (only one boss and just a few 6 chests). Just like Void’s Edge, there’s 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 it’s got some of the best legendaries so it’s 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 hadn’t run it into oblivion because of Nova’s monotone reading of the Sentinel’s messages) and those damned golems are the most annoying enemies in game (they’re 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 can’t 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). It’s 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, it’s 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 it’s the “final” mission of the game, the difficulty is appropriate, imo.
If I had to choose a favorite, I’d probably pick Archive. It doesn’t 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 don’t run it as often).