Omega is for those interested in combat. The story itself is weak. It will also give you a lot of items and experience points.
From Ashes can be completed in about 30 minutes or less. It´s really short and the strong point is the prothean/collector weapon, very useful both for you and squad-mates, and a new character that will offer many different iterations both inside the ship and during missions. Bringing Javik together will offer new insight in almost all of the missions. His presence can impact story scenes so much that I would recommend 2 different plays at least, one without him installed, and one with.
Citadel is drastically different from the rest of the game. It has a new mission, filled with comedic elements, The combat simulator is also very cool. And there are lots of interactive segments with your old and new squad-mates, and a chance to reunite them in a party.
Leaviathan has a very intriguing story and interesting combat. There are also some puzzle-adventure elements that enrich the experience while you play detective. It also has a great music score. Even thought Edi and Vega are the most important elements of the narrative, all squad-mates will have exclusive content and comments, including Javik. And later, near the end, while talking to the last character you encounter you will be able to ask more questions.
I would recommend all of them, except for Omega. This one was a big letdown. Not even the fact that is has new exclusive enemies (something that only Citadel can also claim) helps reducing the disappointment. And the fact that it´s Shep alone with Aria and a new Turian female (no squad-mates) does not help.
You can always start watching someone on youtube playing and then decide if you´re enticed enough to purchase.