With Uber/Lyft, my advice is to have both apps on your phone and price-check your rides. Most drivers drive for both companies. About the only ones who don't are those who rent the car they are driving through one company and are therefore limited to that company.
If you put the apps on both of your phones, you will potentially get double promotions. With the promotions, be sure you understand them. Sometimes promotions are market-specific, so if you get a promotion at home it might not apply at WDW.
The reason I say use both is that the two companies both use dynamic pricing. If one is busier than the other (common), you may get either a) a quicker pickup with one, or b) better pricing. Both companies have an abundance of drivers in the Orlando market, and especially in the WDW area. You should not have significant waits for rides. One big key to timely pickups is NOT to move after you order your ride. The driver's app shows where you ordered the ride from and if you move after ordering that can create all sorts of problems, including cancellations.
It's also important to understand the driver/rider rating system. Both companies use a 5-Star system, but many riders don't understand how it works. 5 stars is an "A," but 4 stars is an "F!" If a driver's average drops below 4.8 (a 96 average if you're in school), they are on the verge of termination. So always give a driver 5 stars unless there is something significantly wrong with the ride.
I also tip in cash -- NOT in the app -- for several reasons. First, it's an immediate "Thank you" to the driver, and they know immediately that it came from you, not some other rider. Tips are appropriately identified with rides, but not until later when the driver has time to look over their days results. Tips are also not always posted immediately, so cash is better.
Secondly, Lyft often actually counts in-app tips against drivers if the driver is working on a special promotion. Lyft's promotions are usually "guarantees" that the driver will achieve a certain amount of pay for a certain time period. The problem is, they count in-app tips in that guarantee -- which means they pay less in guarantee if the driver falls short of what they promise. In other words, with an in-app tip you could effectively be tipping LYFT, not the driver. It's messed up, but that's Lyft. Uber doesn't play games with driver's tips.