I am a current part-time Uber driver in Orlando.
The Uber app will not allow you to request an Uber on MCO property. What people do to get picked up at the airport is to take a free shuttle to one of the nearby hotels. Once they are at the hotel they will request an Uber. This is perfectly OK. Some people will drop the pin somewhere outside of MCO property and then call the driver and explain that they want to be picked up at the airport. I personally won't pick up someone at the airport if they do this, but others will. I have no problem picking up someone at one of the nearby hotels.
Uber can pick up and drop off anywhere on Disney property. At first, some of the parking booth attendants would ask Uber drivers to pay, but they have stopped that (or at least it happens less frequently). I have an annual pass so I just show that if I need to get through. I have never had any issues. At the MK, pickup and drop-off is easy because there is dedicated 15 minute parking. At the other parks it is a little more tricky, so you need to call your driver to confirm the pickup location.
Taxi rates are $2.40 a mile. Uber's non-surge rates are 75 cents a mile plus 13 cents a minute. An Uber vehicle is almost always cleaner and you will never get taken a longer route than necessary. The downside is that you might have to wait a few minutes for an Uber to show up, whereas taxis are usually waiting for you everywhere on Disney property.
You would think more people would use Uber, but they don't. It's so much easier than taking the buses, and it's not expensive. For example, if you wanted to go from the MK to the Animal Kingdom Lodge you would pay about $20 in a taxi. That same ride would cost about $8 in an Uber, if there was no surge. Even if there was a surge, it has to get to 3.2 in order to get to the same rate as a taxi.
If you do take an Uber, remember that the tip is NOT included. It's not the driver's fault that Uber has not included a tip button. If you can tip the bellman to put a suitcase in your trunk, it is OK to tip the driver who takes your suitcase out of the trunk and drove you safely to your destination. I realize that some readers might find this controversial, but if you can tip a taxi driver why won't you tip an Uber driver? Again, the service is usually superior and the vehicle is much nicer and cleaner. If more people would tip, there would be more drivers, and riders would not have to wait as long when they request a ride.
Also, any rating less than 5 stars means you want your driver fired. No, it doesn't make any sense, but Uber will deactivate drivers with less than a 4.6 rating. So, anything less than 5 stars is unacceptable, according to Uber.
If you have any more questions, please feel free to ask.