I owned a pair of nice Shure in-ear monitors, too. I much prefer the 770s to them (Now the Shures go to the gym with me for workouts). The reason I went looking in the first place is that the in-ears didn't reproduce bass very well and I was overcompensating for their shortcomings. That became obvious when I played the tracks on any other system, as the bass tended to drown out the other parts.
I can't speak to the M-Audios, though. They could do a much better job.
They do, the bass is stunningly accurate, and never puffy, like all over ear headphones.
In fact even the high end shure`s have amazing accurate bass response