Just about every THer has a slightly different opinion about coil size.
Here's mine.
The stock coil is the best size for the intended purpose of the detector. Most machines are made for general coin shooting and the stock coil is a compromise for most coins. The majority of coin finds are the memorials/wheats, nickels and dimes. The stock coil is the best size for these smaller sized coins (best depth + target separation for the most popular targets in the U.S.A. = the stock coil). In fact, if you contact any company (that bothers to respond to the public) you'll get this same thing from them (because that's where I got it).
Now, what about smaller or bigger coils?
Smaller coils are for greater target separation and smaller targets than the average. These always get less depth than the stock coil when it comes to the average coin finds.
Bigger coils are for greater depth on targets larger than the average stock coil finds.
As a rule, you can figure about 1 inch of depth to each inch of coil diameter (round coils, the others are more tricky to figure). However, this is not for all sized targets. The stock coil will go deeper on a target in it's range than will a larger coil built to function at maximum on targets larger than the stock coil's range.
Coils are antennas and the antenna must be factory tuned to the target. Larger coils are less sensitive than stock coils are when it comes to targets within the stock coil's range. However, targets larger than the stock coil's maximum depth range will be detected deeper with the larger coil. The antenna's (the coil's) physical size almost always means greater depth (not always) IF THE COIL WAS DESIGNED FOR THAT TARGET SIZE AND ALLOY.
And then if this weren't confusing enough you have the difference between the so-called "wide scan" coils and "concentric." The deepest coils are the "concentric." The widest area coverage coils are the "wide scan" (thus the name).
A round 10 inch "concentric" coil will usually detect a silver quarter at 10 inches deep (it depends on the quality of the detector's electronics). This same coil may detect a clad quarter at 12 inches. The type of metal is also important. But in some soils this same coil may not detect a clad quarter 4 inches deep (this is another factor).
Confused?
I've seen it where a 6 inch coil got better depth than a 10 inch coil on any size target due to iron masking (another factor). In some soils a big coil is nearly worthless due to taking in too much ground area at a time.