A 1" sensor has a surface area of about 116mm². A 1/2.3" sensor has an area of about 28mm². That's over 4× the light-gathering area. This is a huge advantage that is pretty much impossible to overcome — see Why does it seem like large sensors are necessary for good low-light performance?. Or also see the last part of this answer: Can a smaller sensor's "crop factor" be used to calculate the exact increase in depth of field?

Perhaps you are wondering about the density of pixels, with 20mp vs 12mp. Generally, either of these provide enough pixels to produce high-quality large prints, so the sheer number isn't really an issue. While it's theoretically true that larger-sized individual pixels can provide higher quality, at similar print sizes in the real world, this isn't a huge factor (see Do megapixels matter with modern sensor technology?) — and more importantly, any differences here are usually less important than generational differences in sensor technology, and completely dwarfed by differences in sensor size — there may be a 20% improvement or whatever, but that's nothing compared to the fourfold improvement from 4× the sensor size.

And of course in this case, the individual pixel size advantage goes to the larger sensor anyway.

But, I should stress that this is only going to be a big factor when looking for high technical quality in challenging conditions. In most circumstances, both of these cameras are capable of producing amazing photographs.