Well...why don't tell us what microphone it is?
Basicly, if no effects are used, there should be no difference in the microphone sound whatsoever between DAWs.
I can't think of any way it could be possible, but maybe someone else knows.
Your soundcard changes the audio into 1s and 0s and sends the exact same digits to any software, and all music software produce practically the same sound from the same data.
Have double checked there's no track EQ or whatever involved in either software?