I have been in your shoes (well, not your shoes), so I can offer what I learned from my experiences.
May, Sept., & Dec. 2010:
After paying $200 for our Gracco tandem (front/back) stroller, we weren't going to let that money go to waste. I have to say, as the oldest DD got bigger, the stroller was that much harder to push. In Dec., our oldest DD (4 3/4 y.o. & 15 mos. @ time of travel in Dec.) only weighed around 35 lbs., which made pushing the stroller easier. However, after folding that thing up and carrying it on & off the Disney busses was "becoming a nightmare" (to quote my DH who was always in charge of this part).
March 2011:
We decided to give renting a try. We rented a City Mini Double stroller from Magic Strollers: parents loved the ease of pushing/folding it up (much lighter than the tandem), but oldest DD didn't like sitting next to her sibling (5 y.o. & 18 mos. @ time of travel). If we could've afforded it, we would have bought a City Mini Double and ended our time with the tandem (that's how much we liked the side-by-side).
Oct. 2011:
Since we didn't have it in our budget this time, we opted to bring our tandem, again. By this point, DD's were 5 1/2 y.o. (41 lbs.) & 26 mos. (backseat weight is negligible for our tandem), and we ended up telling the oldest "to get out and walk" because it was too hard to push. In fact, the only time she sat in the stroller was to take a quick snooze or if the crowds were too much. Also, myself or DH would walk in front of the stroller for fear of clipping a strangers heels & feeling the "stroller wrath" rained upon us. With the side-by-side, we could gage our distance better and didn't feel the need to walk in front of it.
Nov. 2012:
Renting a double stroller from one of three sites. I know my DD6 won't really sit in it as much (as evident from last trip), but there will at least be an option for her. If we only brought a single, the girls would fight over it.
My DH and I thought about bringing two singles (similar or not) and tying them together. But after pondering it for a bit, we didn't really like the idea of having to fold up two strollers & oldest DD was too big for any lightweight umbrella stroller anyways (plus, heaven forbid one parent was left with both strollers to navigate).
FYI: Disney does have a size limit for strollers, which cannot exceed 52" in length & 36" in width (although many doubles out there exceed this by a couple of inches), & must be able to collapse.
CONCLUSION (finally): If it's in your budget, rent a side-by-side. However, I would take a single stroller for airport use (if you're flying). You have a while to decide and test out your tandem in a crowd.