I would assume that normal simulation training would provide some general cross-training, so the pilot of one type could move to another with only limited disorientation. Basically, I would expect them to be able to perform all "simple" tasks without any significant trouble, but probably suffer penalties for difficult actions in an unfamiliar ride.
Essentially, I would treat their piloting skills as one worse for some period of time (1-2 weeks?), and if the weapons configurations are considerably different, add a gunnery penalty only for the things that are different. If the change is expected well in advance, allowing for simulator time to familiarize themselves with the new unit, reduce that to only a couple of days in the cockpit to become proficient. Someone who "grew up" with a family 'Mech, rather than taking the normal and more general course of formal training on a variety of chassis types, might take a lot longer to readjust, because some things may need to be "unlearned".