The simple answer is that a transcutaneous incision must be made if there is excess skin and muscle to be removed; this incision (properly performed) leaves a virtually imperceptible scar right below the eyelashes, and allows access to trim, reposition, and properly release eyelid structures, precise surgical maneuvers impossible via a transconjunctival approach. That is why this is considered the "standard" approach, and the one most commonly used by most blepharoplasty surgeons, regardless of specialty. This (transcutaneous) approach may also be necessary in an "excess fat only" patient who, in the surgeon's best opinion, has poor skin tone that will sag and deflate if fat is removed via a transconjunctival approach without some sort of skin tightening, perhaps by laser or chemical peel as other options to excision via scalpel.
If, however, the patient is young, has great skin tone (good elasticity), and only excess fat pad protrusion, the transconjunctival approach leaves no external scar, does not violate the orbital septum or lamellar structures, and reduces the (slight) risk of increased scleral show, lateral lower lid "rounding," or ectropion. That is why some surgeons who like this approach say it is "safer." In skilled hands it truly is a very safe operation, though it may lack the detail and finesse the open-incision approach allows, but with higher (still low) risk of lid malposition and corneal drying.
The best way to answer this complex question is to state that no one approach is best for all patients; each and every patient has unique age, genetics, skin/muscle elasticity, healing, and scar tendencies, and all of these need to be taken into account when recommending a procedural approach. Beware any surgeon who states "I always" or "I never" because that is just not possible for every patient.