According to RideGuru, it would be about $13 for UberX or regular Lyft and about $20 for UberXL or Lyft XL.
Which is better depends on where you are, and what you need. In many markets Uber will have many more drivers, with the result that your pickup will be quicker.
In WDW however, Joel's answer above is perfect -- they're the same...except for child seats if you need one. And his advice about having both apps on your phone and checking both prices before ordering is also perfect. RideGuru will give you a general estimate -- the apps will give you a very accurate quote at that moment.
If you need ONE child seat, Uber has some vehicles with car seats. The additional cost is $8 more than the prices above. Lyft has no vehicles with child seats.
There is also Disney MinnieVan, which can carry 6 and has TWO child seats. MinnieVans are $15+ $2.75 per mile, and are ordered and paid for with the Lyft app. That ride is 8.2 miles, so MV would cost about $38.