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My newtonian gives refractor-like star images, so I don't see a difference there.
But, where seeing is concerned, the 4" does see better seeing but that is simply because it cannot resolve the seeing fluctuations. If the average seeing is 1.1" the 4" won't see a change, but the 12.5" will see mediocre seeing.
The seeing is the same in both scopes (as long as equally collimated and cooled), but the 12.5" resolves the fluctuations better.
And if the fluctuation enables a resolution of, say, 0.3", the 12.5" and 4" will both see excellent seeing, but the 12.5" will resolve much smaller details. Seeing where I observe is always fluctuating and is often much better than 1", so usually surpasses the capabilities of the 4" in resolution.
It has been 17 years since I owned a catadioptric scope (unless you consider a newtonian with a coma corrector a catadioptric), so I cannot compare. The large secondary does have an effect in reduction of resolution, but even there, a larger aperture will show you more.
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