You'd have to fold it up for the train at MK too - or leave it parked and make the whole circle around the park and come back to it.
The last two years we took our Mac Volo strollers and LOVED them. We went back to the resort during the day for naps, so reclining wasn't an issue. There were also a couple of times DH took one DS and I took the other. (Then there were times too that we left the strollers in one area and just walked around all together.) The two umbrella strollers made the couple of late nights back on the bus, very manageable. Also, the two umbrella strollers were VERY easy on the MK train and on the little train at AK.
Also our boys preferred riding in the strollers - which they hadn't done since right after they turned 3.
I never missed our jogger stroller at WDW (wasn't an option as we had sold it about a year before).
I think you'll be fine with either option. (If you are going to take them in the airport to gate check, the umbrella strollers fit through the scanners, so you get through faster than a jogger. Not an issue if you check it or drive)
If you are considering umbrella strollers and don't already own them, I won't buy the $10 models - you will get tried of pushing and wish you'd brought your P&T.