Rather than starting anew, I figured I'd post a short little review of the new DLC just released this week. For those not paying attention, it's called Burial at Sea (Part 1) and it takes us back to Rapture in the 50s.
The Good: It's more BioShock Infinite gameplay. What's not to like? Courtnee Draper and Troy Baker return as the primary voice actors and are as excellent as ever. This DLC is the beginning of a deeper exploration of Elizabeth's character.
The Bad: It's short, and there's a lot more trucking around and exploring/hiding/fighting than there is narrative. The bits and pieces of narrative don't add all that much to what we know from Infinite itself either, until the very end and a bit of a reveal.
The Details: We get a new couple of plasmids/vigours, the weapon system returns to BioShocks original format (i.e. once you've got one, you keep it in inventory), and in general the atmosphere is returned to Rapture. It just feels rushed in terms of the experience; as I said, it's quite short, so you just start getting into it and its over. You also don't have any of the original vigour upgrades or Gear (new gear too, some is pretty cool though), so the old tried-and-true tactics no longer work as well. It is MUCH harder than the original game; I played this on 1999 Mode and unlike the main game, I spent a lot of time returning to checkpoints. Ammo is scare, EVE is scarce, health is scarce... yeah, you get the idea. It's much like the feel of SS2 in that way. The combat is quite unforgiving early on, but later it becomes significantly easier.
In general, I don't think this can be judged on its own; it is clearly the intro act to the much larger Part 2 to follow (in which we play Elizabeth), and should probably be judged in that regard.
Recommendation: If you have the Season's Pass, you have it already and should play it. If not, wait until Part 2 is released and then read the reviews for it. They're a package deal it seems.