I personally enjoy the multiplayer, but there's a huge issue with the servers. Even when the game was relatively new, I'd experience lag quite frequently, and I have a decent connection. I played about 6 months ago, and it was even worse; so I can imagine that's still the case. At this point, it's pretty much only worth playing if you're going for the achievements, unless you have an uncanny ability to tolerate lag.
As for how it is despite the lag, it's not too shabby. It borrows quite a lot from the CoD formula, such as loadouts, perks, attachments, etc, but is still its own beast. The weapons are balanced well, and there's just enough variety. Much like the single player, there are a plethora of ways to get kills aside from the guns, such as hacking turrets and vending machines, plasmids, (interesting combos are possible as well, such as shocking a geyser trap to make it an insta-kill) and Big Daddy suits, which spawn randomly and make the lucky player who gets it a juggernaut. There are challenges much like Call of Duty, and it also features a similar rank-up/unlock system. The gametypes are varied and fun, and none of the maps are dodgy.
All in all, this was a great effort at multiplayer that would have been much better had they invested in better servers. It was a lot of fun in its heyday, and I'd still be playing it if not for the lag.