25MP (or any resolution) full frame sensor with a (say) 1.8 lens will gather more photos than 10MP (or any resolution) APC sensor with a 1.8 lens.
Noise only matters in the context of output. If you’re printing—again just an example—a full magazine spread, the noise level in the final result isn’t fundamentally affected by whether the sensor was 30 or 50 megapixels; FF or MFT. Either way it is ultimately scaled to the print size and print resolution. Nobody except the photographer cares what the noise looked like at 100% pixel zoom. All that matters is the relative appearance of noise in the final product.
Thinking about the individual pixels of a sensor is tempting but causes an unfortunate chain of erroneous assumptions.
It is true that (a) larger sensors have had an historical efficiency advantage, but it's progressively diminishing, and (b) larger sensors tend to be capable of lower area-equivalent ISOs. If you could build an MFT sensor capable of ISO 25, and used comparable glass, the full frame advantage would be eliminated.