Hey Dan
These are some of the differences off the top of my head.
IABSM is card driven for actions
MP is impulse driven (ie…Germans have 5 platoons and the Russians have 7 platoons, then the first 2 activations the Germans will activate 1 platoon and the Russian will activate 2 platoons, then 1 each until the end of the round)
Like most lardy games they are bucket o' dice for to-hits (if I remember correctly) then +/- modifiers
MP is based off Troop quality. Green, experienced, vets, etc… all have a base Troop Quality. I think "green" is 10. So, you'd roll your D20 and +/- all the modifiers and try to roll UNDER that end number.
Direct Fire combat in IABSM for armor (if I have this right) is roll 2 D6 to get your to-hit result (+/- some modifiers if I remember) and then roll firepower dice and then the opposing player rolls their save dice? I didn't like this system personally.
Direct Fire (tank vs tank) in MP has a couple different mechanisms. They have this thing called Offensive Modifiers.
OM1 – firing while not moving. This can be a -2 to +1 (gun optics, crew quality, etc…)
OM2 – moving/firing. This is always a – modifier
OM3 – gun stabilizers. Some late war Shermans had this I think.
There are other modifiers of course like cover, etc….
Roll a D20, +/- OM, +/- other modifiers to obtain your to-hot number.
If you hit you look at the Kill Table. Compare your Offensive Value (this could be AP, HE, or some special ammo) and compare it to the targets Defensive Value (side, rear, front, top armor value). Take that difference to find the column you roll on the Kill Table, roll your D20 to see what effect happens (1 hit, 2 hits, immobilized, etc…)
That's what I know. I've played IABSM a couple times and while it's a decent system I dislike the bucket o' dice mechanic and I thought the armor rules were lacking.
MP has a few more dice rolls, but I find the armor rules a little more detailed.