MOSFETs or even better IGBTs proved to be easier to work with for the fast switching applications. Remember that in the setup like Bedini's MOSFETs are used at the primary side where we still operate with "conventional" electricity. Of course there is a point of self adjusting oscillator function done with bipolar transistors but that can be tweaked to be done with MOSFETs of IGBTs as well.

On the secondary side of the Bedini setup the things are quite different and I found that MOSFETs and IGBTs are prone to random latch-up, self-triggering and sudden death regardless of the fact that their maximum ratings weren't exceeded. The rules of engineering on the secondary side are changed and sometimes the proven circuit setup simply doesn't work. I have a theory on why it happens and in what circumstances but I prefer to keep it to myself until I'm certain of it.