The size of the objective lens determines the amount of light that is admitted, and therefore, how 'bright' your view will be. For example, a Simmons 30mm objective compared to a Leica 77mm will be like looking at a target at dusk compared to a target held in a searchlight. You'll be able to see holes at 300yd with a Leica 77, you won't hardly be able to find your target because of mirage with the Simmons 30.
When faced with the choice of a Simmons 50mm or a Leupold 50mm, go with the better glass lens (Leupold); the image will be more crisp and clear. You'll be able to see the rings on your target at 200 yd with the Leupold; you probably won't with the Simmons 50.
(Take into consideration that my specific scope examples except for the Leica 77 are hypothetical. I don't know if there are Simmons 30's and 50's nor Leupold 50's out there; I'm just using hypothetical examples.) My suggestion is to go to a big camera store or nature store (like REI) and sample the different scopes; the camera stores around here allowed me to leave my wallet and let me take a scope out to the sidewalk to check it out. Look at things like long-distance license plate screws. Remember that they'll be at least twice as big as a .30 hole.
A friend and I did a side-by-side; the Leica 77 (no Televid) are really great; try and find one to test. You can find them used with the angled 20-60x eyepiece for ~ $7-800 with some patience; that's not much more than a new Kowa.
By the way, for definitions, I'll do my best:
field of view: the measurement (expressed as a diameter) of how much of the object area one can see when looking through the scope
Eye Relief: either a minimum or maximum distance from the eyepiece that one must maintain the eye, in order to see the entire field without parallax
Parallax: the layman's version: This phenomenon is manifested optically as the 'shadow' around the edge of the field of view as one looks through the scope. Adjustable parallax scope allow the user to 'adjust out' most of the shadow around the edges. Eye movement/placement adjusts the rest.
Exit pupil: expressed in millimeters usually, this is the size of the image at the eyepiece end. As I recall, the human eye cannot expand any larger than 7mm (?), and any larger image inherent in the eyepiece is wasted.
Objective diameter: size of the front lens (theoretically the larger the better)
Close focus: the minimum distance that the scope can resolve objects