Theoreticaly the advantages are--less bullet distortion=better accuracy and easier cleaning (thats all I can recall right now) . Disadvantages shallower rifling=more prone to wear/damage, harder to get cast bullets to shoot well.
That being said, I have had several marlins in.357, .44 mag, .30-30 and .45-70, all with micro-groove and all shot with more than acceptable accuracy, most were very accurate (with receiver sights or scope) and all shot well with cast bullets.
FWIW, 44Bore