Never flown a fighter jet, however I always remember an interview with Israeli ace Giora Epstein (pretty sure he was the one although it was a while back) who fought more than 10 migs at once, at one point alone, shot down a few and came home. At one point in the interview where he describe the KFIR vs the F-16. While he would rather have the F-16 vs modern fighters in a furball, he always preferred the non FBW feel of the KFIR and how he felt he had way more control of it near the edge so could push him and the aircraft to it's limits.
I also loved his comment on the question about how he felt facing so many migs at once. His answer was along the lines, you can only have one on your tail at any time, and that is the only danger, so I just watched out for that one, and shot at others that came up in front.
I've heard similar comments in regards to Air Force pilots that prefer the Hunter to modern aircraft for similar reasons. Obviously this is from a connection with the aircraft and handling, not from an effectiveness in battle point of view. I doubt any of them would opt to take a hunter into battle over an F-22 vs an PAK-FA or such for many other reasons.
Even if you wanted to throw a modern airliner around to test it's handling you will hit a wall of computer generated nope at some stage, and the places you can go with the computer turned off/restricted will probably kill you.
I've had the pleasure of doing maintenance shake downs on some transport category, was quite weird to practice some steep turns and throw it around a bit outside of the simulator. All my years of flying it straight made me feel like something was wrong in doing it.