the ballbot is a dream for every robot builder. Your work is very very interesting.
In my previous works I used the Kalman filter and a PID control to make a self balancing robot.
I think that only an Arduino Uno or an Arduino Duemilanove is enough.
In my tests the whole cycle, with Kalman and PID control, was made in 4-5 ms. So the frequency is 200hz.
The most heavy elaboration is the communication with serial port to print values, for examples acceleration value or something else. My advise is to use always the max speed (115.200).
For the execution time the best is the complementary filter instead of Kalman filter. The results in my experience are similar. I made same tests about it (http://www.gioblu.com/tutorials/sensori/193
). The text is in italian, but google translate is your friend.
For the LQR control, I don't understand. The LQR gains are calculated with the Matlab, so they are constants. Or you are speaking about on-line dinamic calculation of LQR coefficients ?