In the Orlando market, especially in the WDW area, you won't find much difference in the pickup times or quality of rides between companies. The market is very saturated, which is good for riders.
Most drivers do drive for both companies simultaneously. The exception is those drivers who rent their vehicle through one of the companies; they are locked into one company.
You can get fare estimates either on RideGuru or from the company websites. Before you actually order your ride, you will see an actual fare quote on your app and that will be what you pay unless something unanticipated happens.
I recommend having both apps on everyone in your party's phones, because pricing and promotions vary between the two companies. With multiple Uber apps on several phones, you can switch around depending on who has a promotion they haven't used and save some money.
Outside of the Orlando market, you may see a significant difference in the companies depending on market. In most markets, Uber is much stronger than Lyft, but that's not true everywhere. Typically, tho, Uber has many more drivers and many more riders, so pickup times are usually quicker with Uber...outside Orlando.