It is simplicity itself for jet pilots to fly today's training aircraft.
In flying right seat to jet experienced pilots both for type training, and formal test flights in GA types, this has generally not been my experience. I know that there are pilots who are excellent at crossing aircraft classes, but I never assume that any given pilot has this skill. Sure, the systems management skills are much more complex for jets, so pilots with that skill will surpass a GA pilot in that area. On the other hand, handling a low inertia plane, flying entirely power off approaches, effectively recovering unusual attitudes, judging a non paved surfaces for landing suitability, or flying a deliberately non stabilized approach may not be strengths fresh with jet pilots. Foremost, it has been my frequent observation that most jet pilots I've trained or mentored in GA types, either overlook keeping the ball in the middle, or at best, really have to focus on the task.
I make no assumptions about the skills pilots from other aircraft classes when flying GA with them - good or bad. But, I don't "sit back and relax" either, until I am actually confident in that pilot's skill based upon my observation. A pilot telling me that they have 10,000 hours in a jet does not provide me complete assurance while flying GA with them.