I do know a scope tends to perform the best in the middle mags, or at least not in the extremes of its mag range. The 5-25 does darken rather significantly between 20x and 25x, and that’s another consideration if that happens to the 3-20 at 20x.
Carbon - Since you tagged me above I'll give my 2c on this... (plus 200c more since it got long winded)
It looks like you want to know if the other scopes will get darker at 20x because its on the upper end of the power. This is what I'll address.
Why does the image get darker at higher magnification?
When we zoom in at the higher magnifications the image appears to get darker. This is not a failure of the scope and glass but this is a failure of our eye and our brain processing the light it sees. As we increase the magnification the beam of light (exit Pupil) of optics gets smaller. When the diameter of this beam of light get smaller than the pupil of our eye, extra light is let into your pupil. You brain has to process this extra light in the image and it makes the scope image look darker.
Example of this. Take a picture (no flash) of someone standing in front of a window. If the window is smaller than the the person and they block all the light coming in the window we can see the person well. (exit pupil larger than your pupil, no extra light gets in). If the window is larger than the person and light comes in around them and in the picture (no flash) we see a very dark image of the person because the background light if changing how the camera processes the light. (exit pupil smaller then our pupil and extra light gets in)
Calculate your Pupil Size.
We can figure out if another scope will be bright or dim by calculating the size of our pupil and compare it to the exit pupil of another scope.
Pupil size is calculated by dividing the objective diameter by the magnification (Dia./Mag) Example: 56mm Obj / 25x is an exit pupil of 2.24MM
We can figure out our pupil size by using our current scopes. If at 20x the image is nice and bright, 21x is still pretty good, and at 22x the image is starting to grey or fuzzy, we can back calculate to get our pupil size. 56/20=2.8mm(bright) 56/21= 2.66mm(good) or 56/22=2.54mm(grey). We would need al least a 2.66mm or larger exit pupil for us to see a clear, good, image.
Things to Note - The size of our eye's pupil changes and is effected my several things.
The more ambient light, the more we will automatically restrict our pupil size. On sunny days our eyes constrict to make the pupil smaller, on cloudy days our pupil opens more, at dusk our eye start to open even further to let more light in. In the dark our pupil is wide open to help us see in the dark the best we can. (When the room goes dark we say "I'm letting my eyes adjust". This is the pupil changing)
Age - the older we get the harder it if for our eye to constrict the pupil size.
For these reason try to do test your pupil size under the conditions you will be using the optics the most.
Will the New Scope have a darker image at 20x?
Now that we know the limit of our eye's pupil (2.66mm) for a good image we can calculate the exit pupil of the new scope at to see how it will work for us.
A 5-20x50 scope will have an exit pulip of 2.5mm at 20x. This is smaller than the 2.66 we need and the image will be darker. With this 5-20x50 the exit pupil will be 2.66mm on 18.8 power (50mm/2.66mm = 18.78) We'll be able to see clearly until 18.8power but the image will be darker at above this value.
Final Thoughts
The scope's image does not get darker because of the scope mechanics or glass quality. It gets darker because our eye and brain have to process more light information. Don't blame a scope for a dark crappy image on max magnification, its the human procces making the error.
Don't use high magnifications in darker conditions, our pupil is getting bigger so we need more light out of the optics to cover our pupil.
I hope this helps, have a good day.