My experience is that MF pairs very well with Dynaudio (out-of-the-box). Also, like many here, I never heard a MF amp sounding bright. While changing cable might help, you should realize that M3 is not a young amp anymore. Re-cap-ing it might have a much more significant effect.
Regarding the original question, while MF M3 is a very good amp it is certainly possible to better it. Accuphase is the first brand that comes to my mind (e.g. E-408 or E-450), but there are quite a few other brands you can consider, e.g. Simaudio, Octave, ASR, Bryston+ a tube pre, etc. All these brands pair very well with Dynaudio speakers. What is your budget?
Finally, regarding the NAD M3 integrated, as already mentioned it is not in the same league with the MF M3 integrated. A few years ago I have compared a NAD M3 integrated with a MF A5 in the same room driving a pair for Dynaudio Contour S1.4. The A5 literally moped the floor with the NAD. With less demanding speakers the NAD probably had the edge when it came to detail retreaval, but the NAD was not able to provide the juice required by the Dyns.
Regarding the original question, while MF M3 is a very good amp it is certainly possible to better it. Accuphase is the first brand that comes to my mind (e.g. E-408 or E-450), but there are quite a few other brands you can consider, e.g. Simaudio, Octave, ASR, Bryston+ a tube pre, etc. All these brands pair very well with Dynaudio speakers. What is your budget?
Finally, regarding the NAD M3 integrated, as already mentioned it is not in the same league with the MF M3 integrated. A few years ago I have compared a NAD M3 integrated with a MF A5 in the same room driving a pair for Dynaudio Contour S1.4. The A5 literally moped the floor with the NAD. With less demanding speakers the NAD probably had the edge when it came to detail retreaval, but the NAD was not able to provide the juice required by the Dyns.