I don't own either but if you take a look at the frequency graphs between the M3 and the M22 then it is a Yes and No answer.
The M3 has a bump that carries well down after the apx. 150 Hz range but after 70Hz it starts a much deeper nose dive. What that should translate into is that the M3 will 'appear' to have more bass in in your types of music (pop & rock) because it's louder in the bass frequencies that are most common in popular music. The drop off for the M22 is not as severe but typically only dance music plays regularly down there and portions of classical pieces.
Once you get big drops in SPL, those frequencies begin to get hard to hear anyways if the rest of the music is drowning it out. Bass is funny so it's a bit different but essentially. the graphs start to lose some significance the further down the frequency chart you go because once you can't hear or feel something, the graph become irrelevant. However, they still do say something towards the design goals.
In short, this matches what I have heard here. That to make a general statement, the M3s are a good choice for pop/rock music if you are planning to hold off on the sub for a bit. This is due to the bump where we tend to notice it the most.
However, the M22 is no slouch either. If you are adding a sub anyways, you might benefit from the linearity of the M22 across the board. The sub will handle the deeper areas areas better than either speaker anyways.
Actual experts should be along shortly along with people with real world experience to share.
