Ours were four and five last trip. We also stayed at BW and rented strollers. They did fine getting to and from Epcot on their feet (we'd often wait for the boat on the way back). We often park hopped and never had any problem getting a stroller - lines were minimal (look for the stroller express line before MK opens - pay for your stroller out front, then pick it up inside the gate).
Its amazing how much energy little kids can find. They can go longer than I can - its just channeling that to productive walking instead of jumping, dancing, spinning and squirming! Fortunately, Disney provides great motivators for moving in terms of "walking to the next ride." My daughter often wants to be picked up - but she doesn't need to be picked up - its a want. When its a need we rest. Or I pick her up for about fifty steps then say "you need to walk again, honey" and she is fine.
Its a rare "personal" stroller that will fit two four year olds. My daughter was over 45 lbs and we'd have had to buy a stroller for her - as she outgrew her toddler Graco a few years ago. Not worth it for us. The Disney strollers have their issues (not great for small kids, and, yes, with the rental fees you could buy a nice stroller and resell it when you get home!) but are nice for bigger kids - they push 100 lbs of two kids easily. The other thing is you don't have to worry about it getting stolen - if its missing, you go back to stroller rental (not convienent, but still) and show them your receipt and get another one! Strollers don't go missing often at WDW, but when they do, it can put a real crimp in the vacation
As for identifying your rental stroller - this is especially important if your last name is even vaguely common. We often get off and see two strollers with "Peterson" on the back of them.