Of course each microphone sounds different. Because each mike has a different construction, different values for their electrical, mechanical and acoustical components, sometimes different working principle, which causes to have entire different electro-mechanic-acoustic circuits. That's why they have different frequency responses, and there are other factors too like distortion, saturation and non-linearities.
What I would do in your place is to try to find the frequency response curve for each mike, and then try to equalize each recording with the inverse-response of the actual mic response.
For example suppose you recorded with a Shure SM58. Given a SM58 frequency response like this:
Try to equalize the recording like this:
Doing this, each recording should approximate to a flat and uniform frequency response.
It will be a bit hard to achieve such a precise equalization. I would try to mix both parametric and graphic eq.
Needed to say, because of the proximity effect, the response itself of a mic would depend of the distance between the source and the mic, used for recording. So try to choose a response curve that would match the distance used for the recording process.
Also is needed to say that even a batch of microphones, of the same model, will have slightly different responses. So each microphone has it's very own response. So the ideal would be to measure the response for each mic, but that requires a reference measurement microphone (for example the Earthworks M50). But these are expensive and the procedure to measure the response of a mic is complicated.
Even the most professional mics like the Beyerdynamic M88TG comes with the measured response for the actual unit, with matching serial number.