Most important branch of the U.S. Armed Forces

[Redalgo]

I'm going with the USN on this one. It can guard shipping lanes, enforce blockades, strike inland targets, wrest air superiority from the air forces of most other countries, engage in electronic warfare and surveillance, deploy SEALs, destroy inbound missiles, and - though to what rate of success I don't know - take out nuclear warheads descending toward coastal cities or military assets before they can detonate. The Navy arguably provides the most effective, most difficult-to-counter nuclear deterrent, and is essential to both projecting hard power around the world and preventing other countries from ever putting their troops' boots on our ground when it comes to conventional warfare. One might say we're much like the UK insofar as being an "island" power.

[Redalgo]

And the Navy doesn't have a better air force than the Air Force.  And I'm not sure why this myth persists.  Landing on a carrier is impressive, but it's not like USAF pilots couldn't do it if they were trained to do it.  Average fighter pilot to average fighter pilot, it's probably pretty close between the two branches, but the USAF has MUCH better birds and a lot more of them.

And to reiterate, the USAF owns space and cyber warfare.  Two very important battlefields going forward.

To be clear though, I was not under the impression that the Navy has a superior air force to that of the USAF. Our best-performing birds, when measured along the lines of most mission-relevant metrics, cannot be launched from aircraft carriers. And so far as I am aware there is not a big gap (if there is one at all?) in quality concerning the pilots themselves when it comes to skillfully, professionally accomplishing mission objectives. However, we do not always need the best of the best hardware because the air forces of most other countries have much less experience and/or significantly inferior birds to contend with. We fight all our wars in developing nations these days.

On the other hand, I am somewhat biased because of my policy preferences for closing down American bases abroad (which inflates the importance of the USN in terms of force projection) and working multilaterally with other countries on humanitarian interventions where I imagine the USAF would oft occupy a secondary role of logistical support rather than being at the tip of our spear, so to speak. Under these conditions the States would not remain a superpower militarily without having a clear measure of dominance at sea regardless of how far the fleets travel from home.

Looking ahead, I do see wisdom in your points concerning space and cyberspace. In general, I reckon that future technological developments will inevitably make control of the skies - not of the waves - the single most important factor in proficiently projecting American hard power and protecting our economic interests. There will someday come a point at which naval assets become an utter waste of taxpayer money useless refashioned to serve out their traditional charges in space instead of under or atop of the water. For the time being though I am pretty comfortable with considering the USAF the second most important branch of the armed forces.