They all have different play styles, so it depends on what play style suits you best. Sure some classes are overall better or worse, and that may change as you level but its really what fits your play style. Adepts are really suited for people who like staying behind cover to pop up occasionally and throw a power. That is where they are strongest, and if you play like that they are fairly solid once you get your cool downs short enough and the durations of singularity long enough. Other classes like the sentinel really excel at the run and gun game, they feel weak if you hold back and fight like an adept.
Now if you say best = who blasts through a map quickest it is probably not adept. Adepts also seem more reliant on having the right team to make it through a level relatively quickly. You want people who can help you out in comboing your biotics and people who can drop defenses quickly.
Adept is by far my favorite class to play and I like the play style. This does not change the fact that I have to play it safer than with other classes and there get out of jail free card is a short stalling effect and doesn't help much when your cool down is still long. Other classes are better for when you get sloppy, lazy, sleepy whatever you want to call it when you screw up and getting pounded.
If you set up your position correctly in the beginning of the fight though and position your team mates well they are really powerful.
I have yet to try engineer so I don't know about them. But incinerate for armor, shield damaging powers, combat drone is awesome when I have Tali so it would be more awesome on a shorter cool down, AI control is useful as well, I think I could smote people fairly well with them. I might give it a shot.