Image quality is highly correlated with pixel-size. A larger pixel accumulates more light during an exposure of a certain duration. By having more light, there is less noise in the image because the pixel gets more signal from light and noise is relatively stable. So proportionate, which is what we perceive, images are less noisy.
Larger pixels also have a larger well which is the capacitor that accumulates the electrical charge that photons release when they hit the sensor surface. These deeper wells allow a pixel to represent more dynamic-range. It is applicable to scenes of high contrast, where smaller pixel reaches its maximum level faster and clips image highlights.
Now, technology has created a lot of optimizations for it such as BSI (Back-Side-Illumination) that allows silicon of the same size and number of pixels to effectively have larger pixels because more photons landing on the sensor get used, so pixel size alone is not an absolute measure, but it is far more accurate than resolution.
When comparing two cameras, what you can look at is the pixel-pitch which some sites list in specifications or you can estimate it yourself. Taking a full-frame sensor of 36x24mm and divide it by resolution (Say 26,000,000 for the 26 MP 6D Mark II) and compare it to 22x15 for Canon APS-C (or 24x16 for APS-C of other brands) and divide by the resolution (Say 32,000,000 for the Canon 90D). It is not necessary to use exact numbers because there are a lot of factors at play (which is why a 24 MP APS-C camera today gets better output the a 24 MP of 10 years ago) but this pixel-size calculation gives you good idea of relative quality.
Now if you were to take an image from a certain sensor and scale it down, you are effectively simulating larger pixels, there is more noise usually than if the sensor had a lower native resolution. So, if you want to compare at equal print sizes, you can divide by the resolution you intend to use for a given print size.
Camera makers know this which is why some - and Fujifilm had a particularly clever way of doing this - bin pixels to simulate larger pixels. They essentially group a number of pixels together, typically 4 (in a 2x2 grid), and output one image pixel for each 4 sensor pixels. This improves image quality at the expense of resolution.
Addendum: As someone pointed out. Lens has a great impact on image-quality. This comparison is purely from a sensor design but if a lens cannot deliver sufficient resolution, then output quality gets reduced but it does not affect noise or dynamic-range. Again there are subtitles since some lenses can have such strong vignetting that they effectively diminish light which makes noise apparent in peripheral areas.