Forget Apple vs. Google . The fiercest battle in the tech capital may well be between two heavily financed upstarts plotting the demise of the taxi industry—and each other.

Uber Technologies Inc. and Lyft Inc. operate just blocks from each other in San Francisco, yet their bitter war has spilled into dozens of cities where they are racing to provide the default app for summoning a ride within minutes.

The two rivals are undercutting each other's prices, poaching drivers and co-opting innovations, increasingly blurring the lines between the two services.

But this is more than two tech darlings duking it out. It's a battle for a key role in the future of urban transportation. Many commuters now rely on Uber and Lyft to get around rather than taking cabs, buses or trains and, in some cases, their own cars.

The loudest opposition to the ride-sharing apps comes from regulators, taxi drivers and local taxi commissions, which have moved to ban the companies from operating, offering proof that a multibillion-dollar transportation industry has entered a phase of rapid transformation.