I've got one- i have a 308MXLR, 338MXLR, and a 45-70 1895XLR- all with 24" barrels.
there are good recoil pads on the MXLR's I would say the recoil is less than the 45-70, but a little more than the 308 Marlin Express, probably similar to a .308 Win more than anything.
I have only shot mine with open sites, haven't mounted a scope on it yet, so i'm not the best one to ask about groups at 200-300 yards. My 308ME is deadly accurate at 100 yards (less than 1 inch 5shot groups with Hornady LE ammo) I would suggest you visit Marlin Owners - Index
there is a forum just for 308ME/338ME owners, lots of good info there.
The pic is my 308MXLR (.308 Marlin Express) with a Leupold VXII 3-9 scope