I use Xtol, Rodinal and D76 in inversion tanks and Jobo.
Xtol seems to be pretty insensitive to agitation, i.e. I need to reduce the time by maybe 10% going from tanks to rotary and the film speed is unaffected. Rodinal seems more sensitive to agitation; it needs significantly reduced development time to keep the contrast under control and has about a stop of speed loss when using it rotary. It's still great stuff though.
Replenishing with a rotary process isn't generally a great idea because of the increased oxidation; that's not a problem if you do it one-shot.