The only difference is they use a smart phone app as a dispatcher.
This might be a complete shock to you, but the app is not actually the only difference between Uber and a taxi company. That being said, having an automated dispatcher itself is a major benefit over taxi companies, unless you like it when your cabbie calls you from across the city to say he'll be there in half an hour.
Face it, Uber is successful because they are doing the job of taxis far better than the taxis do it. Like any other industry that has been around a long time, taxi companies got lazy and quality plummeted. I don't even want to think about how many cabs I've been in that had shredded seats, sticky floors, smelly drivers, etc. One example that sticks in my head was a driver who was in the range of about 400 pounds and had his seat back far enough that there were maybe 6 inches between the back of his seat and the seat behind him, so no one is going to sit there. He sure as hell isn't moving his seat if 4 people need to get in the car though. When I think of taxi rides, it's those experiences that I think about. Long waits, bad cars, angry drivers, etc. Uber solved all of those problems at once. I can see where all of the cars around me are, when my ride gets accepted I can track the car to where I am, I know the driver's name, license plate number, make and model of the car. I can talk to the driver before they pick me up. When the ride is over I just go, I'm not sitting there dicking around with payment. I can also track the entire ride, I've called Uber cars for women leaving my parties and I've tracked her the entire way home. If anything got shady I know the driver's name, license plate, phone number, last location, and car description. And, without exception in my experience, every Uber car I've had has been as clean or cleaner than any cab. I've never had an Uber vehicle in poor condition, and after the ride I can rate the driver. If the driver's rating goes below a high threshold then Uber does not give them any more jobs, so the drivers and vehicles need to be presentable and agreeable if they want to keep working.
If taxis want my business again, all they need to do is match the service I get from Uber. This is what the largest taxi company in Phoenix thinks about mobile apps (for reference, at the time of posting that page says nothing except "Sorry, the offer you tried to access has ended."). For most taxi companies the concept of a mobile app means being able to order a taxi without calling. I'm not interested in that, I want the convenience and accountability that I get from Uber. Taxi companies don't want to compete with Uber though, they just want to outlaw them and go back to their monopoly.