Not much in it, the .303 is a 2300 fps high velocity "crack", whilst the M-H is a 1320 fps "whumph", Paper patched rounds actually make the M-H quite a pleasant round to shoot, compared to modern big oversize cast bullets. The original buller was about pure lead and 12% tin, diameter was .451 which is just over bore size of .450", once wrapped in 100% cotton fibre paper it went to .459", the rifleing picking up the paper, not metal/metal, the paper too was dipped into beeswax, to serve two purposes, waterproofing and lubricaton.
With a full load and patched bullet I would expect to fire 30-40+ rounds at the range on a morning, in a shirt no problem.
Fouling and leading will cause a modicum of increase in recoil, however a properly patched and lubricated round will scrub fouling away each round (that's what it was designed to do), In a .303 this is not an issue as the powder burn is almost complete, the .303 bullet is metal jacketed, firstly in cupro-nickle, later copper, there is no lead fouling. The reason why it is copper jacketed is a) lubrication (soft), b) it stops the lead bullet breaking up in mid flight due the huge centrifugal forces.
A M-H carbine, with the correct 70 grain load and 420 grain patched bullet is a bit more jumpy, however compare this to a No5 .303 Jungle Carbine, and that old boy I can assure you is a beast, even with a soft rubberised buttpad, 50 years on and theose buttpads are have now lost thier cushion, and it shakes yer filling loose.
I can liken a M-H to a 12 bore shotgun.