As far as cleaning goes, I don't think there's much difference.
I clean my rifle by pulling a bore-snake through it after firing it hunting (ususally 1-3rds) just to prevent residual fouling from attracting moisture and causing rust/corrosion/pitting. At the end of the season, I remove lever, bolt, and extractor and give the barrel a good cleaning with bore solvent, brushing, ect. same as conventional rifling.
However, if I'm going from shooting jacketed ammo, to cast bulleted ammo, I WILL give it a much more thorough cleaning by wrapping a bore brush with a patch and soak it with either JB-bore paste or Remington Bore Cleaner and work it through the bore to remove most if not all the copper fouling. This results in the bore conditioning to shooting the lubricated cast bullets much quicker, resulting in much improved accuracy. I likewise do this with all rifles before shooting cast bullets after having shot jacketed bullets. Removing the copper fouling makes a big difference in accuracy.
The only really different consideration I give to the MicroGroove barrels is to use a larger than normal cast bullet. I've found that a .311" bullet is vastly more accurate through my MG barreled .30/30 than a .309". And, I get equally good accuracy through my .308" .30/06 with the .311" bullets, so, thats what I size all my .30's cast bullets........
After initial check of zero before the hunting season, (I do this each year because sometimes I'm switching loads/bullet design/ect from one year to next) I don't do the extensive cleaning as I feel that a super clean bore, and/or lubricated bore will make the "cold shot" effect of the first shot from the barrel to be further exagerated. I like my bore to be previously "fouled" so that accuracy of first shot is enhanced (or more correctly less affected). Hence, I feel that by just pulling a bore-snake, or just a clean dry patch with a rod, is sufficient for "between" hunting outings.
Others may have differing opinions, this is mine......... and it "works" for me.