Difference with Amazon is the barrier to entry to creating a worldwide distribution business is far, far greater than creating a ride hailing app. Amazon was losing money to invest in valuable real estate and buildings and other big ticket capital items that retain worth, whereas Uber is basically giving away subsidized rides hoping that people will pay more in the future.
I spoke with an Uber driver about this recently, and one of Uber's barriers to entry is their phenomenal data on roads. As an example, they know for every apartment complex, where you'd drive around inside to drop off food as oftentimes you can't just go to the front. Or which parts of a road have no stopping zones along with the schedules. Bus stops too. And the app will guide you to get a pickup where the Uber driver is actually allowed to stop.
Drivers are interested in those features because it makes them more efficient. And having a critical mass of drivers is what makes it possible to get a ride in a few minutes. There are other upstarts, but they don't have many drivers, and your potential user market doesn't scale linearly with drivers because nobody wants to wait 30 minutes to get a ride (even with crazy discounts).
I am an Uber driver. I'm sure they have the things you describe in some places. Where I am, the app regularly tells me to drive off the side of a bridge because it believes there is an at-grade intersection in a highway. Despite my repeated reports of the issue, it persists. All the Uber maps in my area are at least 1-2 years out of date and are nearly useless for navigation. I pretty much ignore them a lot of the time.
This was one of my experiences with Uber versus some other ride hailing apps. The Uber app seemed to understand the airport and would help guide me towards a pickup zone and help me relay to the driver what pickup zone I was going to be at, while at least last time I used them other ride hailing apps tended to just try and show wherever I was at the time.
Amazon and Uber are definitely different, but in 2003 Amazon's market cap was about $21B, or ~$36B in today's dollars. Uber is actually bigger than that in value today (~$144.11B).
Amazon was far from a dominant player in 2003, and AWS wasn't launched publicly until 2006.
From a product standpoint, as others have stated, Uber is a real-time services marketplace vs Amazon which is more about physical goods (again, excluding AWS, which is technically a service). Most of their value is putting all the work into the ground to keep the marketplace balanced, which is a tricky marketing and econometrics problem. One need not look farther than Lyft to see how hard it is to keep the "5 minutes away or less" guarantee.
Also to those who think the app is a non-trivial technical achievement, I would recommend reading some of the blog posts that go into some of the crazy technical challenges they hit [1]. Specifically in some cases, in order to make the app work in all geo's, they ran up against practical limits to binary size at Apple. Not to mention that geo / waypoint data is a genuine "big-data" problem and not easily reproduced by just any company.
