Divide the objective diameter by the magnification and the result is the exit pupil, the size of the beam of light (the image) being projected into your eye. The bigger the better, up to a point. 7mm is typically the biggest iris opening a human eye has, and as we get older, that gets smaller. So in your 20s, 7mm may be worth having, but in your 40s you may be able to use only 4 or 5 mm.
That's why traditionally 7x50mm binoculars were the standard for maritime use, because they would be doing watch at night, (50mm divided by 7x magnification = approx. 7.1mm exit pupil.) Of course on a variable magnification scope, the exit pupil varies with the setting.
In comparing scopes, all else being equal, the larger the objective bell, the more light that can be gathered and a 30mm tube allows more of that gathered light to be transmitted to the eye than a 1 inch tube would, but all else probably isn't equal.
The dimensions offer potential light gathering and light transmission, but a manufacturer can waste some of that potential or make the most of smaller dimensions depending on the quality of the glass and the quality and type of coatings on the lenses and the finish on the interior of the tube. (I'm not suggesting Kahles don't use top quality glass and coatings - at their prices, they should be right up there.) If your pupil can only dilate to 5mm, like Ridge Runner said, a 7mm exit pupil is partly wasted, and you would get a better picture from a manufacturer that made you a 4x20 scope and put in top quality glass and coatings than from someone who just jumped on the bandwagon of 50mm objectives and a 30mm tubes and didn't pay attention to the quality of glass and coatings. And it doesn't matter how big the objective lens or the tube is if some other part of the mechanism fails.
There is a fashion for larger objective bells and now the larger 30mm tube which is probably driven at least in part by the expensive and revered European brand names like Zeiss, Swarovski, and Kahles, but in Europe there is probably proportionally more hunting in the dark than there is in N. America and it may not be what you need. (I myself even have a Bushnell Trophy model with a 30mm tube, but I bought it because I like the magnification range on the particular model and the uncommon reticle it has and it was on sale for a price appropriate for the applciation I had in mind.)
