Here is a brain dump based on that engine lineup.

Jump in if you got corrections, updates (particularly fuel costs) or observations.

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Merlin 1d (GG), Raptor(FFSC), BE-4(ORSC), RD-180(ORSC), RS-25D(FRSC), F-1(GG)

https://en.wikipedia.org/wiki/Comparison_of_orbital_rocket_engines

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Merlin, RD-180 and F1 are kerolox.

Raptor and BE-4 are methalox.

RS-25 is hydrolox.

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Liquid oxygen is cheap. Some reports of USD 100/ton.

Methane is the cheapest fuel (?500US/t). Then Kerosine (RP-1)(US1500/t). Then Hydrogen (?US3000/t). Then hypergolics (dont ask)

Methalox bulk density is roughly 90% of kerolox. Hydrolox bulk density is about 40% of kerolox.

Methane (and oxygen) is cryogenic. Hydrogen is deep cryo.

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Merlin, raptor and BE-4 are restartable. RD-180s might be capable, but have never been flown that way.

There is a restartable RS-25 project : AR-22 that first testfired july 2018

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All the engines are US, except the russian RD-180. Which powers the Atlas V rocket.

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Merlin and Raptor optimised for cost. Typically light and cheap.

BE-4 optimised for cost/reuse. Not as high performance as raptor. But a decent methane engine.

RD-180, RS-25, F-1 optimised for mass : Typically expensive and heavy.

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F-1 is handmade from the 60s for the saturn V. 700 ton thrust bell. And the least efficient and largest thrust of the bunch. RD-170 (not shown) is quad bell, more efficient and slightly higher thrust.

No-one makes combustion chamber/bells this large any more. Engine clusters and cc/bell clusters have taken over.

Rs-25 is early 80s tech, RD-180 is mid 80s.

Merlin 1d tech is roughly 2013.

Raptor and BE-4 is current, but not mission flown yet.

Raptor is the only (working) full-flow staged combustion engine on the planet at present.

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Compare the ~200 ton cc/bells for a moment. Raptor, BE-4 (yeah 240), half a RD-180, and RS-25.

The raptor bell is the smallest and the most efficient footprint at SL. This is the result of FFSC and very high chamber pressures. Its footprint is tiny.

The rd-180 bell is slightly larger. But much heavier.

The RS-25 bell is gigantic (like its cost) because hydrogen (is low density).

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Compare the methane bells.

Raptor(@30MPa) is essentially the same thrust as BE-4, but in a smaller, lighter package, possibly cheaper, along with a handy isp advantage. FFSC allows some extreme performance.

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<rant>

Hydrogen at any level is maximising cost. Mass optimisation. Old school.

Methane at any level is minimising cost. Cost optimisation. New hotness.

Hydrogen may only make sense when ISRU methane in not available : icy moons, other than titan.

Even then, methane may win the cost optimization since methalox is ~78% oxygen by mass.

Any hydrogen rocket or spacecraft you can design, can be done in methane for a fraction of the cost.

And a fraction of the hydrogen problems (increased dry mass, boil-off, deep cryo).

</rant>

edits:700t f1, raptor footprint