I drive for both companies in Miami, have ridden with both companies, and have both companies' rider apps on my phone.
In the Orlando market, I recommend that riders do exactly what Allison recommended above -- price check every ride.
Both companies use "upfront pricing" which means that their prices for the same ride will vary somewhat depending on a variety of influences including demand. Both companies may also have "surge" pricing at peak times (like park closings) and those surges may vary widely. Demand is NOT identical for both companies, so you will see price differences.
Almost all drivers drive for both companies, so in most cases you're dealing with the same driver and riding in the same car. The Orlando market is very saturated, so you will not have long waits with either company.
If you are concerned about safety, all rideshare drivers have passed very stringent background investigations mandated by state law. Both companies also double-track each ride in real time -- via the driver's app and the rider's app. Both companies provide an option to share the progress of your ride with trusted friends/relatives in real time. From a safety perspective, Uber's suite of safety features is somewhat more robust than Lyft's, but both are good.
Both apps offer secure payment by credit card (and other options) and detailed receipts to document charges. No credit card info is stored on your phone.
Before you put either app on your phone, check for promotions. Both companies frequently offer promotions -- but know that most promotions are market-based, so a promotion in your home town may or may not be usable in Orlando.
