Just a quick question. Theoretically, if I have a 10" RC f8, the resolving power with the camera would be, say 0.4". Will it be any difference ( in resolving detail, splitting stars... etc ) compare that with 10" Newtonian f4, but using drizzle x2 integration during processing ?
Of course the RC will require a FF, and Newtonian will require a coma corrector, and I assume ideal situation for optical performance.
It's actually not as simple a question as you might think to answer.
First, fast optics often have compromises in terms of their resolution even on axis. To get good off-axis performance (using a field flattener, a reducer, etc.), the designer will be balancing loss of on-axis performance with gains in off-axis performance, so the Paracorr that you are using to get a nice flat, coma free field out of the 10" Newt will, at least a little bit, damage its resolution in the center of the field of view. The amount of damage might be quite small, though, to the point of being immaterial. For example, I would say that my 12" f/3.7 telescope has essentially the same resolution on-axis as my 12.5" f/8 scope. It's hard to know for certain since I can't run them on the same night, but if there are differences they are quite small.
You asked for a bit more than that, though. You asked whether you would get the same resolution with the same camera using drizzle. Probably not, but the devil as always is in the details. If your 10" f/8 scope is sampling at 0.4" per pixel, then you could probably switch to an f/4 telescope at 0.8" per pixel and notice little if any difference. That assumes your seeing conditions are the typical 2" to 3" that a lot of us seem to run into. The consensus seems to be that if you have 2" skies, you will get benefits with smaller pixels down to about 0.7" per pixel or so. After that, it's not just diminishing returns, but undetectable ones. If your skies on a given night are significantly better than 2"--it can happen!--then you might get significantly more out of the f/8 scope of the same aperture.
The next thing to keep in mind is that optical quality matters, and slower scopes are generally easier to make at a given level of quality than faster scopes. It may not be a huge difference between the two scopes you mentioned, though, since Newtonians only need one asphere and a flat while the RC will need two aspheres, and the primary will be quite a bit faster than the overall telescope, maybe faster than the parabolic primary in the Newtonian. For these two particular telescopes, either might be the better optically.
A lot of people seem to think that aperture doesn't really matter once you get past about 5" or so (at least in terms of deep sky imaging since it involves long exposures). Seeing determines your resolution. The truth is a bit more nuanced than that. All elements of your seeing train have an effect on your final resolution. Diffraction, optical quality, collimation, equilibration, tracking, focus, sampling rate, and seeing all play a role. As your aperture increases, seeing starts to dominate, but it isn't to the point that the other elements don't even matter. Even for long exposures, you'll still get more resolution out of a 14" than a 12", more out of a 12" than a 10", etc. It's just that the differences get smaller and smaller. Those buying larger telescopes are primarily hoping to get better signal to noise ratio in a given integration time, but there are still some improvements in resolution as you get larger all the way through the common sizes of scopes used by amateurs. Diminishing returns, though, in terms of resolution. I have looked back at the resolution I have achieved (as measured in FWHM values on an integrated luminance master) across the various scopes I have used over the years. My 12" scopes yielded a touch more resolution than my 10" scope. My 10" yielded quite a bit more than my 5" scope. My 5" yielded a LOT more than my 80mm. This is after accounting for how good my guiding is/was. As it happens, though, the highest resolution I ever got out of a deep sky image was using the 10" scope. I had one night of particularly good seeing--will under 2"--that resulted in a super sharp image. In general, though, I don't think I would buy a scope larger than 8" or so under my average skies with the hopes of improving resolution. And I have generally achieved the same resolution across a given field of view with fast and slow scopes as long as my sampling was sufficiently high with the faster scope.
Finally, a quick comment on Drizzle... It's useful when you are under sampled, but it isn't magic. If you are significantly under sampled a 2x Drizzle can help significantly, but not to the point of being equivalent to 2x the sampling rate. And if you aren't significantly under sampled, then Drizzle may not help at all. In the cases you outlined (0.4"/pixel or 0.8"/pixel), I would be surprised if Drizzle helped at all. And in terms of signal to noise ratio, there is no question that 0.8" /pixel will be much better. Frankly, if I were at 0.4"/pixel I would be tempted to bin 2x2 on all but the very best nights.