It depends on how old/big your kids are - if they are very young, and will need a stroller outside of the parks, bring your own. If they can do some of the walking, rent as needed. You may find out that you only need to rent at EPCOT and AK. DS and MK are more concentrated parks, meaning there's lots to do in one area.
One benefit of renting is that you don't have to wrangle the stroller onto the busses, and if you can go part of the day without one you don't waste that time in the stroller corrals trying to get to your stroller and then get it out of the tangle.