The whole idea, by the way, of the full-flow combustion is to extract some more energy from the fuel - before sending that fuel to the chamber, and at the temperature which the turbine of the turbopump can tolerate - so that energy could be used for pumps and more pressure could be created in the chamber. More energy than "more conservative" closed-cycle engines.
The pump power is equal to the volume flow (how many cubic meters, or, say, liters of fuel the pump transfers per second) multiplied by the pressure (which pressure is at the exit of the pump). So, it's not the flow - it's the pressure where Raptor has a big advantage over F-1, and that pressure allows to have a better Isp.
And of course the better Isp allows to reach bigger characteristic velocity (or just a velocity in a free space, where gravity or atmosphere don't get in the way) using the same amount of fuel.
The logic goes roughly like that. Every rocket engine designer wants to reach bigger Isp. For that, using a particular fuel, one need to reach bigger pressure in the chamber, and we move from pressure-fed engines (like the first French orbital rocket, Diamant, which had pressure-fed first stage) to pumps, because high-pressure tanks are too heavy. Pumps initially are open cycle, or gas generator cycle, but we throw away enough gases after the pumps' turbine, so next improvement is we get a closed cycle. With closed cycle we can choose to use all fuel or all oxidizer to move the turbine, but as soon as some component is used fully, we can't get more energy for pumps. Eventually we go to the more complex full-flow cycle, which uses both components and reaches the highest pressure in the chamber.
The next step would probably be a detonation engine :) which uses somewhat more efficient process to convert chemical energy into speed, but it's not yet developed enough. We can also talk about more heat-resistant turbines which would allow to extract more energy from the fuel and to increase pressure some more... but there we also have a lot of R&D ahead of us.