It's not about physical efficiency of the rockets so much as it is about their reuse. When you launch a rocket, fuel costs are basically a rounding error - well under a million dollars in general. Nearly all of your costs come from the rocket itself. And before SpaceX we were simply throwing away these rockets after a single use. Well technically the Space Shuttle was "reusable" but the refurbishment required was so extensive that they may as well have been rebuilding it from scratch after each launch. This is why SpaceX's audacious initial goal of reducing space flight costs by orders of magnitude was completely viable.

I think companies will have difficulty competing against SpaceX, so long as SpaceX is ideologically motivated. Right now their goal isn't to make a ton of money, but to create a stable civilization on Mars. So once we start headed to Mars them making next to no profit on launches, beyond what's needed for development and basic sustainability, would be perfectly fine. So you not only need to hit technological parity, but then somehow also go well beyond them in terms of cost reductions - at least if your motivation is profit.