Pilot DAR I'm on the flip side, I have never flown a big piston but it's on my bucket list to do that some how. The biggest thing that I noted going from pistons to Jets is Jets are more sensitive in pitch than props...
also, if you wanna go have real fun try to get a hold of any of the Learjet 20 series because they are fun and a little mischievous. Also, I'm sure you know about Handling The Big Jets...reading DP Davies you will realize that Jets aren't more difficult than props, just different in some ways Jets are easier than props.