Circumcision style is defined by two axes: low-to-high, and loose-to-tight. The four typical combinations are low and loose, low and tight, high and loose, and high and tight. A circumcision does not have to be on either end of an axis; mine, for example, is low and moderately tight. A low circumcision places the scar closer to the glans of the penis, while a high places it further away; low versus high then reflects the amount of inner foreskin retained. Loose versus tight concerns how much slack skin there is, and is usually determined by how much skin is actually removed.
Which style you choose is generally a matter of personal preference. If you wish to retain your frenulum you will need to choose a low style; the inner foreskin will be removed but the frenulum can remain. The inner foreskin retained by the high and tight style would leave a frenulum in a permanently stretched state, while a retained frenulum on a high and loose circumcision would pull the inner foreskin back over the glans and effectively negate the circumcision.
Anecdotally, the overwhelming majority of men circumcised as adults prefer a tight circumcision. A tight circumcision provides better hygienic benefits by ensuring the glans is normally always exposed and improves vaginal sexual sensation by causing the vaginal walls to slide against the penis instead of the penis sliding against itself. By retaining the inner foreskin, a high circumcision may provide more sexual stimulation than a low circumcision. By removing the inner foreskin, a low circumcision may do a better job reducing female-to-male STD transmission, because the inner foreskin acts as an easy entrance point for viruses.
Most men choose a high and tight circumcision. However, for some men (myself included) the foreskin is unusually sensitive, to the point of causing premature ejaculation, and a low and tight circumcision that removes all of the foreskin is a better option. Remember, more penetrative sensation during sex does not mean better sex, it just means reaching the point of orgasm faster.
This forum topic contains an extensive discussion of circumcision styles and their various merits, and is worth reading.
Images below are courtesy of IMC.
Low and Tight
In a low and tight circumcision the inner and outer foreskin is removed but the shaft skin is retained. The scar is close to the glans and the remaining skin is taut when erect. In a low and tight circumcision it is possible to retain the frenulum.
High and Tight
In a high and tight circumcision the inner foreskin is retained but the outer foreskin is removed along with an amount of shaft skin equal to the retained inner foreskin. The scar is further away from the glans and the remaining skin is taut when erect. In a high and tight circumcision it is not practical to retain the frenulum.
Low and Loose
In a low and loose circumcision the inner foreskin is removed but most of the outer foreskin is retained. The scar is close to the glans and the remaining skin is slack when erect due to the retained outer foreskin. In a low and loose circumcision it is possible to retain the frenulum.
High and Loose
In a high and loose circumcision the inner foreskin and the shaft skin are retained but the outer foreskin is removed. The scar is further away from the glans and the remaining skin is slack when erect due to the retained shaft skin. In a high and loose circumcision it is not practical to retain the frenulum.