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The mods they contain. That is the only difference. Basically it's Greh tech, train craft, no mystcraft, no EE3, There are also some other differences in the mods, but I cannot think of them off the top of my head.
Think of mindcrack as the hardmode option. No EE3 a lot of recipes for IC2 based things are a lot more expensive. For example, nano swords need an iridium plate and diamond drills for quarries. Traincraft adds zeplins, which can be fun.
I believe Mystcraft is being added to Mindcrack when the new version with villiager npc trading for pages is implemented. In it's current state it requires cheating in a book or spamming ages to get symbols.
To put it simply: Mindcrack is hard mode (difficult IC2 recipes/no instant teleportation or lossless transmutation)
In more detail;
Mindcrack has a lot of advanced tech, processing and power options- a little reward for conquering the hard mode. (methane boilers, lava can be processed into any base metal)
Direpack offers a few neat features that make life a little easier (instant teleportation/on hand crafting table)
As general mod play goes- there isn't too much of a difference.
See I like the Mindcrack pack but it's laggy for me when it usuallyisn't ever since the update it'sbeen really laggy. so I was seeing what was the difference between the 2 because I might switch to Direwolf.