(I haven't played the Sega Genesis version, but I have seen some videos of it.)
Here are some that I know of (other than the obvious UI and audio differences):
* When an enemy saves against a spell, the enemy takes 1/4 damage in the Genesis version; in the DOS version, 1/2. For example, against an enemy that saves, Implosion does 500 damage in DOS, but 250 in Genesis.
* Enchant Item's SP cost is 50 * bonus in DOS, but 50 + bonus in Genesis. This means that it is much easier to enchant items to high bonuses in the Genesis version than in the DOS version.
* Frenzy is bugged differently. In the DOS version, the loss of Endurance is only temporary, and I believe doesn't actually affect anything. In the Genesis version, the loss is permanent; however, I believe that in the Genesis version, the character knocked out isn't the one who was targeted, but rather (IIRC) the character in front of that character. (The bug (if it is a bug) that causes enemies to lose their resistances and always fail their saving throws for the rest of the battle is present in both versions.)
* The Mega Dragon does not use its breath attack in the Genesis version; combined with the change to saving throws, this makes the Mega Dragon more difficult. (Of course, I have a feeling that particular monster was not intended to be beatable in MM2.)
* There appears to be some sort of memory corruption bug in the Genesis version, which can affect which spells you know; I am aware of no such bug in the DOS version.
(There may, of course, be other differences between the versions.)
For the curious, I know a bit about a couple other versions:
There is an old Macintosh version that seems to have similar mechanics to the Genesis version, particuarly in regard to enemy saves and Enchant Item. It runs under the Mac's windowing system, and the graphics are in black and white.
There is a Super NES version that was released in Europe (didn't make the US; my guess is that it failed Nintendo of America's QA testing). Some bugs include:
* Max HP potion only gives 2 HP (instead of 512)
* Enemies that save against spells take 50 damage (instead of 1/2 damage); this means that enemies may take more damage when they successfully save than when they don't.
* If an enemy frenzies, it won't hurt you.
* Apparently, Finger of Death and Disintegrate (or at least one of those spells) always work.
* There is a critical bug that can cause the game to freeze when you try to load it. This bug is severe enough for me to recommend avoiding the EU SNES version.
There is also apparently a SNES version that was released in Japan, which is different from the EU version. Unfortunately, it's in Japanese, but it looks like it might be very different from other versions of the game.
(Personally, I think I prefer the PC version; the Sega Genesis version is still playable, but I don't like the change to enemy saving throws.)
There are free emulators online of the sega version. All versions of the game have frustrating issues, but I like the DOS version released by GOG better than the Sega version for a couple reasons. First, in Sega there is no front line (in combat) this means leveling up with wimpy wizards in back is just like putting them in front. In the PC version, your armored warriors get to protect the back line. I feel like spells are more reliable on the PC, but I also use an online monster manual to avoid to much frustration figuring out what I can or cannot cast on something.
I like the Sega version better because the UI and the spells can be read in game with ease, the music is better and the graphics are improved. I would love to see another remake of this game. Has anyone played M&M-X? I would like more helpful information on the screen. On the sega the items hide their bonuses... this can lead to mistakes when rushing through your inventory. You don't want to drop a +30 item that looks like a +1 item. That's my two cents. I played the Sega version growing up, and I loved it. If there was a PC version with the Sega EA graphics and music that would be great.