I was, at first, somewhat dreading this DLC. As a very big fan of Infinite and its lovely protagonist, Elizabeth, I became worried that this DLC might unravel some of what I loved so much about the main game. I can now happily report that nothing was harmed beyond repair.
To start off, I will give two recommendations. 1) Take in the scenery; slow down. 2) Consider 1999 mode.
I give these recommendations for a couple reasons. The DLC is both longer than reviewers are letting on and shorter than most player's styles. That is, if you play this with any disregard for the atmosphere and story what-so-ever you should probably just skip it. I say consider 1999 mode because it feels far more polished than it did in the main game. Instead of encouraging the player to horde all their money for incredibly cheap boss fights like the main game did, this shorter trek forces you to plan resources. The decision to buy 6 extra bullets or save the money for a revive isn't as clear cut as it once was.
As for the DLC itself. The game-play feels a bit more refined, as alluded to above, and Rapture looks stunning. Elizabeth looks stunning too, although I admit I'm still a bit peeved she changed so drastically. This is our Elizabeth, from Infinite, and she looks completely different. Proportions, contours, facial features, exc. Unless she paid a visit to golden age Steinman, these changes are out of place. Period. There are other small story elements that also feel out of place but, without spoiling anything, the Bioshock canon ultimately survives the journey and comes out with an interesting tale.
Despite my annoyances with Burial at Sea's rather obvious inconsistencies, I think I actually enjoyed playing it more than Infinite. There are also quite a few brilliantly shocking moments I'm omitting to mention. If you are a fan of the Bioshock series and plan on digesting absolutely everything this DLC has to offer, you will not be disappointed.
*This review based on a single play-through. Will update after revisiting*