I compare to my 6 inch and 10 inch. Nebula and galaxies are noticeable that 10 inch is better. I sold my 10 inch and bought 16 inch!
Small nebulae and galaxies show more detail in a larger scope for the reasons discussed above, the combination of brightness and magnification. A larger scope, within the limits of the entrance pupil of the eye, (eye's pupil at at least as large as the exit pupil), the image can be brighter at the same magnification, the image can be larger at the same image brightness or some combination of the two. But for large nebulae, they may be more easily seen in a small scope.
A couple of definitions:
Surface brightness: Light per unit area, intensity.. .Stars and extended objects are given visual magnitudes, this is the total amount of light from the object or star. For a star, this is a useful number because a star is a point. For an extended object like an planet, galaxy or nebulae, isn't so useful since the light does not come from a single point, it comes from an area of the sky, the larger the size of the object, the more the light is spread out and the less intense the light is coming from that object. The Andromeda galaxy has a visual magnitude of 3.4 but that light is spread out over an area of about 3 degrees x 1 degrees, clearly that is much more difficult to see than a magnitude 3.4 star. The units of surface brightness are magnitudes per square arc-minute or magnitudes per square arc-second. Andromeda has a surface brightness of about 13.5 magnitudes per square arc-minutes. The surface brightness is a much better measure of how easily seen an object will be.
Exit pupil: The beam of light leaving the eyepiece, what you observe. The exit pupil can be calculated a couple of ways, I think the most intuitive is the aperture divided by the magnification. The greater the magnification, the smaller that beam will be. The brightness of an extended object depends only on the size of the exit pupil, the smaller the exit pupil, the dimmer both the object and the night sky will be. This makes intuitive sense because the smaller the exit pupil represents less light entering your eye. At the higher magnification, the object is larger, the same amount of light is spread out over a larger area, it must be dimmer.. Since the amount of light is related to the area of the exit pupil, the relative brightness of two images is the ratio of the square of the exit pupils. A 200 mm scope at 200x produces a 1mm exit pupil, a 200mm scope at 100x produces a 2mm exit pupil, the image of an extended object like a galaxy is 4 times brighter..
If the exit pupil is larger than the observers dilated eye, the observers entrance pupil, then that added light does no good, the light does not enter the eye. The size of your dilated eye is an individual thing, generally as one grows older, the eye becomes less flexible and is unable to open as far as it does when one is young. Typically a maximum entrance pupil, the observer's dilate eye, is assumed to be 7mm but it varies between about 5mm and 8mm.. You can measure it..
Contrast: Contrast is the ratio of two brightnesses. In deep sky observing, one mostly thinks of contrast as the brightness of the object compared to the brightness of the background sky but it can also be used to compare different parts of an object. A good example of this are the cloud bands on Jupiter, they are bright but they are relatively low contrast, their brightnesses are quite similar.
Since the brightness of an extended object is directly related to the size of the exit pupil, increasing or decreasing the magnification does not change the contrast since both the object and the background sky are changed in proportion. A telescope cannot increase the contrast of an extended object..
The contrast of a star against the background sky is a different issue. A star is a point source of light, when you magnify it (up to about 25X/inch) it does not dim, it's still just a point. The background sky does become dimmer, you are spreading the light out over a larger area.. With the brightness of the star unchanged but the background sky dimmer, the ratio of the two brightnesses is increased and the contrast of the star against the background sky is increased. This is useful to know, increasing the magnification does allow one to see stars more easily, to see faint stars that could not otherwise be seen.
The surface brightness of the object is proportional to the exit pupil, this is independent of the aperture. Since the largest possible exit pupil is the size of your dilated eye, the surface brightness of an image can be not brighter than it is naked eye.. Telescopes magnify objects but they do not make the brighter.
Looking at an extended object, this certainly can be counter-intuitive. Saturday night I was enjoying the Veil nebula in my my 4 inch scope and my 25 inch, the exit pupils were both about 6mm.. the views were quite different, with the big scope, I was looking at a small portion of the Veil, a patch about 0.7 degrees in diameter, object was large and details unseen in the smaller scope were quite apparent. In the small scope, the entire nebulae was seen and nicely framed. It was much smaller.. At first, it seems like the image in the large scope is much more intense but looking back and forth between the two, it is possible to realize that they are equally bright, one is just larger.
In some situations, that larger image scale can actually decrease the contrast, make an object more difficult to see, the object can overflow the field of of view and one has no background sky for comparison..
There is lots to know.. I believe that if one understands basic concepts and how they affect the image, then one can make wiser choices in both purchasing telescopes and eyepieces as well as what to use in a particular situation. Knowing that increasing the magnification does increase the contrast of a star against an extended object suggests that if one wants to see a super nova in a galaxy or the central star in a planetary nebulae, increasing the magnification is a very powerful tool..
Some stuff to consider, I hope this helps those just starting out in this wonderful hobby understand a bit more about their equipment and what they are seeing.