While there has been a lot of talk about reflectors vs refractors, I have not seen a good answer to your question. though one person put his finger square on it.
You asked about resolution and resolution is a function of two things and pretty much only two things.
First, there is angular resolution and linear resolution. Angular resolution is used for point sources, but linear resolution i is generally used to describe performance on extended targets (Planets)
While aperture sets the angular resolution, it is focal ratio and focal ratio alone that sets the linear resolution. The linear resolution of at telescope is set by its focal ratio and focal ratio alone. Any two f/10 telescopes will resolve the exact same number of lines pair at the focal plane (180 line pair per millimeter for f/10, 360 line pair for f/5, and so on). Now this is independent of design, quality, or obstruction. Linear resolving power is totally a function of focal ratio. ( I know people will not believe it or will not understand it, but this is in fact the way it works. This is well described in Suiter's Star Testing book and the Telescope Optics books.
Now the bigger question is what happens to those lines when we view them in a telescope, and for that you need to have a way to conceptualize contrast transfer. This is the most fundamental attribute of contrast loss" In the presence of contrast loss, a white line on a black background will appear wider and darker than it really is. A black line on a white background will appear narrower and lighter than it really is.
So, what causes contrast loss?
Basically, four things cause contrast loss:
- The size of the aperture.. A smaller aperture looses more contrast than a larger one due to more diffraction
- The qaulity of the optics.. A less well made scope looses more contrast than a wall made optic
- The presence of an obstruction will reduce contrast as opposied to an unobstructed scope, and this depends solely on the size of the obstruction, which is a function of the size vs the aperture
- Chromatism.. A scope with more chromatism will have less contrast transfer than a scope with less chromatic aberration.
Of these, the most significant is the size of the aperture. A decently made 10" scope with a 33% secondary obstruction will still preserve more contrast than a well made scope with a 4" aperture because the 4" aperture is always limited by the diffraction caused by the aperture itself.
If the obstruction is kept small, even a 6" reflector can maintaining more contrast than a 5" Apo.
They way that contrast is measured is how much the black and white lines become darker and wider (for white lines) or narrower and brighter (for black lines).
Different things affect the frequency (line spacing) differently. For example, fine scale roughness will lower contrast for all frequencies pretty much the same, while a very large central obstruction will lower contrast of the lines with a width of two to four times the width of the Airy Disk of a star.
So, diffracion of the aperture itself is actually one of the largest inhibitors of contrast transfer, and the smaller the aperture (all other things being equal) the more contrast is lost.
So, we have three different components; Angular resolution is mostly a function of aperture, linear resolution is a function of focal ratio, and contrast transfer is the effect on the lines at the focal plane due to aperture, quality, chromatism, and obstruction in the system. This is expressed in how much different width lines would loose contrast at the focal plane.
A perfect scope would show the lines loosing contrast steadily as the got narrower.
An obstruction could cause wider lines to loose more contrast but very narrow lines to have better contrast.
The smaller an aperture the more contrast the lines would loose due to diffraction alone.
As someone said, contrast is the quality that makes an image look bold and sharp. Angular resolution is what determines the size of the Airy Disk. Obstruction, choromatism, and quality are what take the energy out of the white lines and spreads it into the black lines, making them less dark.