I find that the lower power scope works better in low light and lower contrasting environments than the iron sights. I will have to compare them in the moonlight to see which does better a 20 mm 2.5x 1" or a 40mm 4.5x 30mm.
The mathematical answer is as follows Forrest Halley: divide the objective diameter by the magnification in order to calculate the diameter of the light beam reaching your pupil. In this case, a 20 mm objective / 2.5 magnification = 8 mm light beam, and a 40 mm objective / 4.5 magnification = 8.8 mm light beam.
The diameter of the tube, 1" or 30 mm, is essentially irrelevant for an optical instrument as short as a rifle scope. The wider tube advantage is purely mechanical: it offers a wider range of mechanical adjustment for the internal reticle erector. This was originally important when scopes were artisanally mounted on military actions, it avoided having to shim a mount maybe not installed in perfect alignment with the axis of the bore. Recently, the push to go to 34 mm is to allow more "clicks" for long range shooting.
Obviously the lower the scope axis over the bore axis, the less parallax one has to deal with. This affects both long range and ultra short range shooting (a few yards), where a scope mounted 2.5" over the bore axis will result in an impact 2.5" high. That maybe enough to miss a charging buff brain in the very unlikely case you might have to make that shot...
The human pupil dilates from typically 3 mm diameter in full daylight to approximately 7 mm in twilight. This is the reason why traditional 1.5-6x42 European scopes had a 42 mm objective. They provided a 7 mm light beam at dawn and dusk. This is also the reason why 1.25-4 scopes only had a 20 mm objective. They certainly failed to deliver a 7 mm bean at full 4x magnification, but this was largely irrelevant because they were used at the low end of magnification anyway, and could still provide a near 7 mm light beam at 3x at dawn and dusk...
In your case, assuming the same glass quality, the 20 mm 2.5x 1" and 40mm 4.5x 30mm will both provide a light beam wider than 7 mm, hence all the light your pupil can use at full dilation in low light condition.
An additional consideration I would suggest is that if you need to use your scope up close in urgent conditions, 4.5 magnification is close to impractical and even 2.5x is imperfect because magnification really reduces the field of view. In order to be able to shoot very fast, and ideally with both eyes open either running game (driven hunts in Europe) or charging game up close (DG in Africa), it is important to get the low end of magnification as close to 1 as possible. This is why the technological improvement of the last 50 years have focused on getting down from 1.5x, then 1.25x to 1x in straight tube scope used on DG rifles where light gathering is less important than field of you and speed.
Whether 1x glass with red dot is faster than iron sights, I suspect that the answer is "yes" for an aimed shot. I also suspect that the answer is "no" for a pointed shot, shotgun style, really fast really close, which is why the option to detach the scope continues to make sense. As to whether the iron sights are actually aimed or the barrel and front sight are simply pointed shotgun style, is an interesting question...
On the high end, the universal wisdom was for close to 100 years that 4x or 6x (when technology became able to deliver it) was all a big game hunter could ever want.
These are the reasons why the quintessential hunting scope was for 50 years from post WW II to the 2000's a top quality glass variable 1.5-6x42. Near 1x magnification allowed shooting at running game, 6x magnification allowed shooting out to 300 to 400 meters, and 42 mm provided a 7 mm light beam at top magnification at dusk and dawn. These were rational numbers that defined a product designed by engineers who knew what they were doing, as opposed to today's marketing "geniuses" who put on the market scopes that make no sense whatsoever even though slick advertising may make them great sellers
