My truck has AWD, 2H 4H and 4L. When I first got it if I used AWD it would shudder on turns. I looked into this and found that it meant the transfer case fluid needed to be changed. In my truck it's a special fluid "Auto-Trak II" you can only get from GM (not very expensive). I changed the fluid and AWD works perfectly now.
That said, I use 2H whenever it's dry and AWD when it's wet roads or snow. I never use 4H. If I am offroad and it's slick I use 4L.
I use AWD when it's wet because this beast has so much power it will kick the back out easily on a turn. I know full well how to control a powerslide in the rain, and occasionally do it on purpose but my wife would be surprised. So I just set these rules and stick by it, and it works for us.
Not sure if the -360 has autotrak fluid in the T-case, but if it does it's worth trying a fluid change.