Regarding Joel’s drunkness/stonedness:
I remember reading one time (sorry, no cite) that the first MST3K show was done after Joel had stayed up 36 hours straight or something, and so he was struggling to stay awake during the show. I guess he/the showmakers/the audience liked it, so he stuck with the sleepy style.
Personally, I like Mike, but I much prefer Joel. I think he had a better knack for natural delivery. Plus, the sleepiness (or whatever) is cute. 