a subject with a lot of strong opinions, but here's mine:
with three kiddos, i've done both rent and bring own and i prefer rent
1) it saves you travel space if you are driving
2) it keeps your's cleaner than taking your own did i say filthy
3) umbrella type strollers are way too uncomfortable for that length of time for both the passenger and the pusher if they are taller than say 5 7 or so, hubby is 6 1 and i'm 5 10
4) you can't store much on the back of an umbrella stroller
5) you are incentivized to take less to the parks in the first place because you don't want to pack it in
6) if you go to more than one park in one day, just pull your rental slip, take it with you and hand it to the stroller rental personnel at the next park and you get a new stroller for free...
7)napping is impossible in umbroller but fairly easy in rental
8) if stolen just report and they replace for free
9)no stroller to deal with on monorail or tram
on the other side of bring your own:
1) if you are flying, getting around the airport might be easier for all, kid will be easier to track
2) unloading vehicle might be easier with conventional stroller as you can use it as a luggage roller or whatever
3) no rental fees
4) you can pre load your stroller in room night before and plan ahead which they will make you unload anyway to get in park
5) you can use the stroller to get around the resort and other places where one might not be available
6) although your own will get filthy, it will be your filth and i've never had a dirty rental but i guess it's pretty possible
anyway, we'll be renting next trip let me tell ya......it used to be 7 for single 15 for double and we always got the double for the space