This is a wide open question with many variables, age of the user being one of them. If both scopes are set for the same magnification, the 50mm will obviously let in more light. Set for example at 8 power, the 50MM will give the user a 6.25MM exit pupil size and the 44MM scope will produce a 5.5MM exit pupil.
An older person may not perceive any difference because their pupils only open to lets say 5MM.
Where as a younger user who’s pupils open to 7MM in low light will notice the difference.
Every one’s eyes are different, so each individual user, will have there own unique perception as to when, or if there is any difference, and when that difference shows up, as the amount of available light changes.
(from another source)
Exit Pupil Size
This is another important factor in determining how well binoculars work in low light conditions. Exit pupil size is the diameter of the actual beams of light leaving the eyepieces.
It’s calculated by diving the diameter of the objective lens by the magnification. So 10×60 binoculars would have an exit pupil size of 60/10 = 6mm.
In sunlight your eye’s pupil will contract to a size of 2-4mm. But at night they’ll open to 7mm. This varies with your age to an extent. If the light beam is wider than your pupil if can’t all get through, so binoculars with 4mm exit pupil size seem as bright as those with 6mm in daylight. But in poor light your pupils may open to 6mm, so the binoculars with a 4mm exit pupil seem dimmer than those with 6mm.
As we get older the size our pupils open to decreases. An observer in their 50’s may only have pupils which open to 5mm for example. To these people large exit pupils offer little advantage.