What would be the best method for alar base reduction? Wedge excision, or Sill excision? (Photo)

The Ala or Nostrils can be reduced in the size, the amount of flare, or both depending upon the configuration and overall size of the nostrils.   The kind of reduction is determined by the surgeon's design of the excision.  From your pictures it appears you need both size and flare reduction.   This is usually done in combination with a rhinoplasty but can be done as a stand alone procedure under local anesthetic for patients who are just unhappy with their nostril shape or size alone.

 Both methods are perfectly appropriate for the right problem. It is not that one is better than the other, but the important question is what does the patient need. If the patient is only trying to make the base narrow  and reduce the width of the nostrils, then a sill excision will suffice. If the patient is also trying to reduce the size of the ala   themselves, then a wedge excision  maybe more appropriate. 

The technique chosen for the alar base really depends upon what your goals are.  Variations treat the sill or base or both.