Compact Scope Vs. Full Size... What's the Diffrance?

Here's how I look at it. I mount my scopes with the rings as far apart as possible, preferably within 1/8" of the bells. This position also depends on the scope's eye relief and mounting options for the rifle. Mounting in this fashion reduces any canting from errors in the rings or rfile rails. Compact scopes have less space between the bells than full size scopes, thus more chance to induce alignment error. To visualize this take 4 pins and some string, place 2 pins 12 inches apart with string between them. Place the other 2 pins 1/2" from the string at 4 inches and 8 inches with string to each from pin 1. String 1 is your barrel, strings 2 and 3 is the error between rings.

I'll use a short scope on a short range gun, gun with short rails or if I'm certain I can get it perfectly aligned on a light gun.
 
On a compact scope it's usually more critical on eye placement , and exit pupil is smaller so it's generally not as bright . They can also tend to make the image slightly curved looking ....But almost none of these will you notice unless you look at a full size back to back . If the compact fits your needs then I say go for it :) I personally like a more compact scope
 
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"JoeWayneRhea"On a compact scope it's usually more critical on eye placement , and exit pupil is smaller so it's generally not as bright . They can also tend to make the image slightly curved looking ....But almost none of these will you notice unless you look at a full size back to back . If the compact fits your needs then I say go for it :) I personally like a more compact scope
I would add that some of this assumes that all else is equal. For example, my Clearidge 3-9x32 has more eye relief than my PA 4-14x44. It's a little brighter too but the clearidge is a more expensive scope with a slight step up in glass quality. If I compared it to the clearidge 4-14x44, I am sure I would find exactly what you said. 

Some air rifles have the magazine protruding high out of the breach and in general larger scopes require more clearance anyway so it effects your choice of rings. Other than that and the weight, I would typically prefer to choose the scope that has the better glass over the one that has smaller or larger objective lenses. 

The size of the lens is not usually used to choose a scope until it has already been narrowed down to a shortlist of scopes that does what you want. It isn't the first thing you use to narrow it down.

When deciding between big or small scopes, the main question is if you'll be carrying your rifle (eg on hunting trips) or will you be target shooting from a bench. 
 
This is from the perspective of a guy who has worked with lasers and optics a lot. The shorter the focus, the tighter the radius of the curve on the optics. For a compact scope, it requires more curvature in the lenses, which introduces errors and aberrations which are not present in lenses which have a shallower curvature. You can compensate to some degree with more critical quality control and better anti-reflective coatings; but all things equal, the longer (less compact) scope will be a better choice. There is a reason why many astronomy telescopes are long (or fold the image back and forth a few times to have a longer effective length, like a schmidt cassegrain configuration). A more gentle curvature of the lens gives a better result and has less internal reflections and chromatic errors.
 
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