The question you ask is bound to raise some eyebrows among the experts. This a topic that has been hotly debated for many years. There are some surgeons that are particularly passionate about open Rhinoplasty and others that are equally passionate about closed technique. In the end, a surgeon's passion likely reflects his or her own assessment of their work: those that feel they achieve superior results with one particular approach over the other will have a passionate viewpoint.
Given that I perform 99% of my noses in a closed fashion, I may be somewhat biased in my response here. But there are times that I will choose to convert a procedure from closed to open or chose to do a procedure open from the start. Yesterday, I converted a closed procedure to an open one because of a high septal deformity that was impossible to fix safely using a closed technique. Other situations that may require an open approach for me are revisions that are more reconstructive in nature and deviated noses in which the asymmetries are not reliably corrected with a closed technique.
Profile-plasty, in my opinion, should almost never be done open. Extra dissection of the tip structures for the open approach is not warranted if no tip work is being done. As with everything else, there are exceptions.
I feel comfortable correcting most deviations, most revisions, and doing most tip-plasty techniques closed. The swelling reduction after surgery and the constant feedback during the operation make the closed approach superior in my opinion. However, these benefits do not outweigh the small skin incision used in an open approach, especially if your result will be superior with an open.
My advice: choose the surgeon based on the body of work, rather than their approach. Most surgeons are comfortable with both and will choose the type of Rhinoplasty that, in their hands, will result in the best outcome for you down the line.
Best of luck.