Thanks Frederick. No, I am no expert on this stuff. I see myself more as journalist/popularizer for science, technology and computer related topics.

I think something got accidentally shuffled around in the question you asked so I have a bit trouble parsing it. I'll ask by guessing what you ask. You will just have to correct me or clarify if I am not answering properly.

The gain from methane is primarily in reuse, lower cost and complexity. So for the next generation of rockets where we want to reuse as much of them as possible Methane really helps us get there.

Hydrogen burns clean too which is good for reuse, but hydrogen isn't very good for the first stage of the rocket so you end up having to have other fuels as well: Either Kerosene or solid propellant for the boosters. That adds complexity and cost. And solid propellant is something I think is a very bad choice in general. You got zero control which makes it entirely unsuitable for manned missions.

With methane you get a rocket which is not only easier to reuse, simpler and cheaper but also very good for manned missions since takeoff is done with liquid fuel engines which can be turned off if anything goes wrong to prevent a big explosion.

Falcon 9 e.g. have had engines fail and still completed missions. They just cut the fuel to the failed engine and increase thrust on other engines to keep going.

I am working on a bigger article comparing Falcon 9 with the Neutron rocket which uses Archimedes methane engines. It is a really clever rocket design which is why I am excited to write about it and spend a lot of time on it.

In it I will touch upon some of the cool things the Methane engines help you achieve in terms of how the whole rocket is designed and really maximized for reuse.