Frostbite Engine

Personally, MEA is a much better game than many want to give it credit for, it simply wasn't Mass Effect Shepard 4.  The ending of ME3 left a bad taste in the mouths of many people, and they weren't going to give an inch on anything for MEA.  Yeah, there were some weird graphical glitches and odd facial looks which SHOULD have been worked out before release, but personally I didn't have enough issue with them to raise a ruckus and most were patched.

The issue I think stems less from game engine and more from an overconfidence of what the team could accomplish.  It seemed to me they tried to re-create all the lore and character development seen in ME trilogy in one game MEA.  They really should have started smaller, with less people and refined everything as a building base instead of trying to dump 50 bazillion new people on us with fully fleshed out backstories and personalities. 

As an example, lets take Vetra and Liam their backstories doesn't match up with their attitudes and personalities.  Vetra, strong woman, very competent fighter (skill-set more along the line of a front line fighter), very cool under pressure, and yet her backstory is living the the seat of her wits, no formal training in combat and generally all around supply guru.  Liam, backstory of fighter, security specialist, and first in emergency response team BUT he is impulsive, a bit flighty, skirts the rules and generally not very level headed in is loyalty mission.  It is like the writers changed stuff up in the middle of production and didn't go back and correct other things that would also have been effected by those changes.  Swap either backstory or characters between these two people and they work much better for the story. 

I have said it before, I personally think the devs of MEA fell into the trap of comparing MEA to the entire trilogy instead of comparing it too ME1 as it should.  They should have had 4-6 companions, worked really hard on them, spent many hours honing 4 planets and any new races of them, and kept it tighter in story and scope as a setup to later games, like ME1 was. I really don't think the issue was the engine, but instead was the scope of the game they tried to create since they weren't so much building on previous lore as building a whole new Universe to explore.