The Mud Bug is shorter, about the same length as the MD3 XL, but it is wider and thicker. Here is a pic of the molds (top to bottom: MD3 XL, Mud Bug, MD4):

The biggest difference is the size and action. The MD craw claws displace more water. The Mud Bug claws are more active. All are very productive as many on here can tell you. Here are some videos, at the bottom is my summary. Maybe others will share their experiences also.
You can see the MD Chunk in the first video. The MD4 is the same bait, with a tail.
http://youtu.be/_3AnrbkLIXk?hd=1The second video shows the Mud Bug compared to a Paca Craw (the Mud Bug is the first craw, the Paca second).
http://youtu.be/UBfoVw-z3Ps?hd=1The third video shows the Mud Bug swimming.
http://youtu.be/yhpLMoIaa_c?hd=1With all that said, here is my summary of each bait:
1) The MD3XL is the most productive craw I have ever fished - it catches a ton of fish from small to 3 lbs. I've caught bigger, but this is how I would generalize it. It's a big time numbers bait.
2) The MD4 is a kicker craw. It normally catches 4lbs or better, but I've caught plenty of smaller fish on it as well. But as a general rule I use the MD4 on a jig, or MD5 Texas rigged when I'm hunting for a sow. Not to muddy the water, but I also use the Birch bug the same way and it has very similar claws to the MD Craws.
3) When I designed the Mud Bug I was trying to create a bait that was as productive as the MD3XL, but also caught larger fish on a regular basis. Overall, I think the Mud Bug does a fantastic job filling the role of still being a numbers bait, but also catching big fish as well. I've caught a ton of 2 - 3 pound fish and several in the 6 - 8 pound range as well (Texas Rigged or on a jig).
Some say the size of the bait doesn't matter, and to some fish I would agree. With that said, based on my own testing, I believe size and action are relevant to most fish. I've spent to much time on the water with these baits to think otherwise.
Hopefully this helps.
Jason