Well for one thing, when your mic'ing a cab, your getting the sound of the cab itself, plus the sound going to the PA. More speakers delivering more sound is going to sound "bigger" for better or worse.
Even without a mic a 4x12 and 2x12 on stage is going to be louder/fuller than 2 Mackie's..... Of course we can't overlook the issue though that what might sound better/fuller to you on stage, might actually sound worse to those in the audience who might be hearing your cab on-axis, and then getting the PA mixed with that... its a reason why many who do still mic cabs (and yes, plenty do) often have that mic'd cab off stage, in an iso-box etc, because that way the FOH mix has full control over what people are hearing in the venue
Obviously matters are compounded though with acoustic drums, and competing with the bass guitarist.
I'd say you don't have a mic vs unmic'd issue, instead you have a stage volume/mix issue and your hoping that putting more cabs on stage will help fill it. It may, but mic'ing the cab isn't providing any magic, because at the very least, you could shoot a custom IR of your cab and then you've got the same thing.
If you really like the sound of the cab on stage, but still want to deliver guitar in the mix to FOH, why not just have a cab on stage, not mic'd, and then also run an output, with cab block, to the FOH ??? Avoids all the mess of sticking a microphone in front of a cabinet, and from your standpoint, its going to sound the same, since your hearing the cab direct, not mic'd in the first place.