Does self driving technology gain more from the data or the state-of-the-art algorithm?
I'll give a high level answer.

Our Bias on Effort

Although self-driving technology is now on the verge of becoming mainstream, incredible effort has gone into its development. The DARPA Grand Challenge, which helped in this technology's advancement, started in 2004. Imagine the total effort that went into this technology over 13-14 years. Many labs were setup with sole aim of competing in this challenge. 

So when you say that we can't replicate the success in our businesses directly, it is better to ask if the comparison is fair. In your business, have you worked on a single problem to such an extent that many bright minds have worked on it for many years? If not, the comparison is not fair (to your business!).

Self-driving cars are not overnight success due to a single algorithm.

No Single Secret Sauce

Media reporting makes us believe that there's one algorithm that rules the technology, reality is more complex. Check this review paper on the complexity of tasks. There are many modules involved (sensors, perception, planner and control module, feedback loops). Yes, probability and machine learning plays a large part in all modules, but there's no single oracle algorithm. Old workhorse algorithms like Kalman Filters also shoulder heavy workload, but wouldn't get mentioned in the deep learning hype.

Yes large data helps, reinforcement learning helps. But so do rules inferred from manual interventions and control theory and older algorithms.

Summary

Many areas from engineering (classic control theory, reinforcement learning, machine learning) form the basis of self driving cars. We can't copy over the success to other domain easily: there's no single secret sauce but tons of hard work and solid engineering over long time.