Well, Logia users are able to split and reshape themselves painlessly. What an Haki user does is force them to reshape and split themselves, which causes pain and damage. If you punch Akainu with chakra, your fist gets indented in the magma, which is painful to him, but he can easily reshape himself to get read of your indentation.
If the logia user is weak, he might be unable to overcome the damage, so he is unable to heal. If he is strong, he can withstand the damage, and reform once again. Rather than speaking of cuts and what not, it's best to speak about damage and pain in it's pure form. If someone with haki was able to punch Akainu through the chest, he'd take a lot of damage, and then reform. But with, something like, say, a water user, or something strong to magma, it would constantly solidify the magma, making the hole in his chest permanent, which would, in turn, kill him.
I also believe it could have something to do with the difference in Haki mastery of them. Akainu being significantly more powerful is able to negate the blunt of the damage of the attacks, being slightly painful but more of a nuisance than a lethal blow.
