Until about 10 years ago, scopes with large objective lenses were considered cumbersome and normally found on high magnification target/varmint rifles. They still work for that application, but deer hunters are finding value in them as well.
This sounds more complicated than it is. Suppose you pick up a scope with a 50mm objective lens and 10X magnification. At 10X, the scope's exit pupil is 5.0mm (50 divided by 10), and its relative brightness is 25 (5.0 times 5.0). The pupil of your eye is about a 5mm diameter a half-hour after sunset on a clear day, so this would be a fine scope for fading light. Another 10X scope looks as attractive on the outside, costs a lot less, but has an objective lens diameter of 32mm. Performing the same calculations, you can see that this scope's exit pupil is only 3.2 (your eye's pupillary diameter at mid-afternoon on an overcast day) and its relative brightness is 10.24. The 50mm scope is more than 240 percent brighter.
So, if brightness is what you want, you should always get the scope with the biggest objective lens, right? Not necessarily.
The calculations just performed will hold true only if the actual effective aperture of the scope is the same as the diameter of its objective lens. This is not always the case. Some scopes limit the amount of light passing through the internal lens and reticle systems, regardless of the size of objective lens. These scopes may have a 50mm objective lens but only transmit light from a 40mm portion of its center. You might be paying for a big lens while getting small lens brightness.
The legitimate reason for offering a large lens scope with a restricted aperture comes when the efficiency of the lens system provides more light than the human eye can use. There are some high-quality, expensive, variable-power European scopes that provide a full-diameter effective aperture at the high end, but stop it down as magnification is dialed toward the lower powers. One such scope at 6X magnification has a full-objective aperture, with an exit pupil of 7mm. When it is dialed to 1.5X magnification, an internal stop in the zoom mechanism reduces the effective aperture to 27mm. Even at this setting, the exit pupil is 18mm--more than twice the human eye's maximum pupil diameter. Therefore, at its highest magnification, this scope provides a 7mm exit pupil--the highest the eye can use even in total darkness. At its lower magnifications, it offers even more without wasting light.
The first wrong reason to market large-objective scopes that do not provide a full-diameter effective aperture is the relative ease in its being added to an existing product line by simply opening the objective end of the scope and sticking in a large lens without changing anything internally. If a manufacturer does this, it can compete with the other large-objective scopes on the market and charge a premium price without actually offering any performance improvement.