I think it kinda depends not only on the individual but on the conversion taking place
IMHO most people would have little problem in converting from say an Archer to an Arrow (the numbers are simple just add 10 kts) you have the fun of wobbly props and up and down wheels - it honestly doesn't take too long to figure out...
If on the other hand your going from say a 152 to a Bonanza or Mooney then clearly its going to take a bit more thinking about and training time (just speeding up thought processes to stay ahead of the aircraft for a start)
Having said that I know of one bloke who was blatting around in an Arrow pre PPL with no worries and another bloke who has quite a bit of time but is having trouble coping with the extra complexity.