Adept. Here are a few reasons why:-
1) Engineers have a lot of work to do on the battlefield as opposed to Adepts. The following descriptions are from the Mass Effect wiki.
The Engineer is a tech specialist, able to quickly and easily manipulate the environment with specific talents, and repair or modify technical equipment. Gameplay focus is on shaping the battlefield during combat, healing the party, and debuffing enemies (disabling weapons and lowering shields).
The Adept is the ultimate biotic, able to affect the physical world with the power of the mind. Adepts are durable and powerful manipulators of mass effect fields; they can use biotics to violently manipulate objects in the environment, including nearby enemy targets. Gameplay focus is on disabling and debuffing enemies while dealing massive amounts of damage.
Engineers have to perform equipment repairs, equipment constructions, and party healing in addition to battlefield control and enemy debuff. Not to mention the fact that engineers have to spend their time outside of fighting maintaining weapons, vehicles, etc.
On the other hand, an Adept just has to use biotics to debuff and disable enemies in addition to provide barrier reinforcements and biotically enhancing ammunition and grenades. That's it. You don't have to be a grease monkey as an Adept.
I just prefer to do less work.
2) Adepts have a lot more freedom than Engineers.
By this I mean an Adept can be anything. They can be soldiers or just civilians (Grissom Academy's focus is not just to train human biotics for military but to educate them and reintegrate them into society, they are like the Xavier's School for Gifted Youngsters). There are many examples of this in game. Liara is a historian, archaeologist and information broker. Samara is the equivalent of the Asari samurai. Thane Krios is an assassin.
However, an engineer is stuck with being an engineer. They can't really be much else. Almost all those who are of the engineer class in game are either engineers of scientists.
3) Adepts are physically better than Engineers.
One of the fundamental aspects of Adept training is endurance. They have to eat a lot and exercise a lot to use their biotic powers. If you are an Adept, you can munch down junk food and still look good. Can't say the same for Engineers, especially in real life.
Conclusion:-
Between Adept, Engineer and Soldier, I would go with Adept.