"Have Blue Origin got rights to "Big F****** Engine" or has Elon beaten them to the copyright?"
NASA can claim "prior art" from 50 years ago. See "Rocketdyne F-1".
It's a source of wonder to people who remember the moon program that everybody gets so excited about "new" engines when "old" technology achieved so much. Sure we've got different fuels etc. etc. etc. but the physics hasn't changed. The limiting factor in a rocket engine is the temperature that the materials can stand, not the energy in the fuel. I'd be willing to be that in most engines the temperature in the reaction chamber is about the same. Thrust is a matter of how much exhaust gas exits in kilos per second. Efficiency, also known as "Specific Impulse" has to do with the exhaust velocity, which really depends on the molecular weight of the exhaust gases, since the temperatures are about the same. That's why oxygen/hydrogen rockets are the most efficient, the exhaust being mostly H20. Carbon fuel rockets have more thrust because the loss of efficiency caused by heavier product molecules (CO2 etc.) is more than compensated for by the increased exhaust mass, but you only need them to get off the ground. Once in space it makes more sense to use the more efficient rockets. LOX/LH2 are touchy, but hydrazine stores well and is the fuel of choice for long range probes.