I have both, and have had and pulled both over the years. My take on it is the main advantage for me of the torflex style is the fact it allows the floor of the trailer to built lower to the ground. Important for a cargo trailer I had ( made it easier to step into for loading ). Same for a current horse trailer I have. The lower floor height is nice for loading.
I can't say that I have noticed any real difference in the handling between the two types. At least in theory, the idea of the trailer being lower to the ground should result in better handling, but again, for me, from a practical manner there seems to be little to no noticeable difference.
It's true that in time, the rubber rods can and generally do settle and harden. Most folks just replace the entire axle at that time. Common repair when folks are restoring old Airstreams.