First of all -- WELCOME TO THE DIS! You'll find a lot of great info here on just about any Disney topic you're interested in.
I drive for both Uber and Lyft in Miami. In Orlando, I agree with Steve that it's probably a tossup. Both companies have a lot of drivers, so you won't run into the long pickup waits you get with Lyft in some markets.
I always recommend that riders have both apps on their phone, and check both before ordering. The two company's rates are basically the same, but demand fluctuates, so their prices will often be a little different.
About the only difference I see is a single female traveling alone at night. In that case, I recommend Uber because of the better safety features with Uber. With either company, you're very unlikely to have any issues, but you can have a trusted friend/family member follow your ride in real time with either app.
The MinnieVan mentioned above is Disney owned and operated, with Disney CMs (cast members) driving -- and it is ordered off the Lyft app only. MinnieVans are XL vehicles, seating six passengers, but each one also carries two child seats. And as mentioned above, they drop at the bus loop just outside the MK entrance which is more convenient (although Uber/Lyft can drop off at the Contemporary which is close).
The MinnieVan pricing is WAY high: $15 + $2.75 per mile, and that does make it a "maybe once per trip treat" for many visitors. Some trips that might be $10-$12 using Uber/Lyft might be $40 in a MinnieVan.