Price said in his blog that the AI doesn't change it's routine much on the harder difficulty levels, but from what I've seen there are more enemies, they're strategically placed in more compromising/flank happy positions, and they hit a lot harder.
I started off on medium for the first couple levels and found it too easy so I switched to hard (which Im beginning to regret a little now :lol) but the biggest difference I noticed is I'm paying a lot more attention to keeping cover. Not cover so much in the GoW/R6 sense, but more like a consistently roving, stick and move approach. When I enter a new area I notice I try and take a quick survey of the terrain, spot cover points and basically keep as safely mobile as possible (while tactically choosing my weapons and targets). Because you can take a lot of damage in such a hurry and the enemy can either rush or flush you out, you can't stay in one spot but you can't always run out in the open either.