There's a halacha that aveilim shouldn't dance at Hakafos. The way we learn this is from when they had the aravos ceremony in the beis hamikdash...it was considered a great simcha to lay the aravos all around. We therefore learn out that aveilim shouldn't dance at hakafos because of the great simcha involved.

Oh interesting.. never knew thats where we learnt it from.. sh'koyach

True that. At my shul the aveilim do not circle the bimah during hoshanot (ideally, they give their lulav and etrog to somebody without so the minim still get used; an aveil is the one to hold the sefer torah). And hakafot on simchat torah are limited to one rotation. [Personally, I don't understand why it's limited to one and not to none].

Either way, you're showing that the simcha is lessened. [/guess]

Could be. I have no idea.
If I had to guess why "we" (ie at least some, if not many) are stricter that even a mourner do at least some form of hakafot on simchat torah whereas on sukkot he stands without circling hoshanot, I would guess it's at least partially because hoshanot, and the simchah associated with them, are only sourced in sha's, whereas the hakafot of simchat torah are sourced in kabbalah.