Regarding horses vs. engines, what changed the game was not engine efficiency, but the widespread availability of fuel (gas stations) and the broad diffusion of reliable, cheap cars. Analogies can be made to technologies like cell phones, MP3 players, or electric cars: beyond just the quality of the core technology, what matters is a) the existence of supporting infrastructure and b) a watershed level of "good/cheap enough" where it displaces the previous best option.

And roads, and other auto-friendly (or auto-dependent) infrastructure and urban / national land-use.

Cars went from a luxury to a necessity, though largely not until after WWII in the US, and somewhat later in other parts of the world.

There remain areas where a car is not required, or even a burden. NYC, and a few major metropolitan regions, as well as poorer parts of the world (though motorcycles and mopeds are often prevalent there).

It’s both. A steam engine at 2% efficiency is good only for digging up more coal for itself, and barely so. Completely different story at 20%. Every doubling is a step function in some area as it becomes energetically and economically rational to use it for something.