How much more efficient would a moon landing mission be today?

It shares the shell, the engines, the avionics, the attitude thrusters, the autogenous pressurization system, the refueling system, and a bunch of other stuff. It will likely share some parts of the life support systems with their hypothetical Mars transport.

It’s not quite as simple as unbolting the landing fins and leaving off the TPS… but that’s why NASA is paying them a few billion for a custom job. It’s certainly a savings compared to developing the entire thing from scratch.

There will be a tanker variant of Starship, which should be very close to the cargo version. Probably just some stretched tanks, and leaving off the cargo doors, mounts, etc. That might actually be the first version that flies due to the relative simplicity.