Orchestra musicians, like all of us, are people, motivated by all manner of things. Sometimes they want a revered maestro to lend gravitas. Other times they might think a young firebrand will attract media attention and flash. After an extended relationship with a boss of a certain personality, they might yearn for a change: a less verbose maestro after a tiresomely talkative one; an instinctive communicator in the wake of someone cryptic.

Lost in this shuffle can be many excellent midcareer artists, some of whom are not widely known and harder to sell to audiences. Why is, say, the Dutch conductor Jaap van Zweden, 54, music director of the Dallas Symphony Orchestra, significantly better than, say, Manfred Honeck, an Austrian, 56, of the Pittsburgh Symphony Orchestra? Both have been mentioned for the New York Philharmonic job. Two other established conductors under serious consideration, both of them exciting and visionary musicians, may be advantaged by having higher profiles with audiences in New York: Esa-Pekka Salonen and David Robertson, both 56.

If the players are sometimes drawn to the eminences, this stems surely from their student days. In music schools, aspiring musicians come to revere masterly teachers, artists who can pass on lifetimes of insights. Some are authoritarian and crusty, though most students are willing to endure rough treatment to learn the secrets of the art form. Others are benevolent and patient, which is not necessarily more effective. Masters of both types have made it to the annals of legendary maestros.

George Szell was an unapologetic autocrat at the Cleveland Orchestra, serving from 1946 until his death in 1970. He could be dogmatic and impossible. Still, he took an ensemble that had been demoralized by the disruptions of World War II and turned it into one of the finest orchestras ever. The players were proud to work with him. Typifying the benevolent master was Claudio Abbado, a towering conductor who drew distinguished music-making from every orchestra he worked with while being courteous and elegant. The strongly unionized musicians of today might not tolerate a Szell, even if he might be just what they need. In recent years, perhaps envious of the Los Angeles Philharmonic’s success under Mr. Dudamel, the new face of classical music, several orchestras have been emboldened to appoint younger dynamos, like Yannick Nézet-Séguin, 40, at the Philadelphia Orchestra and Andris Nelsons, 36, at the Boston Symphony Orchestra. Sometimes the choice of a youthful conductor works out perfectly. Sometimes (as with Mr. Muti and his current ensemble, the Chicago Symphony Orchestra) an eminence is ideal. The key is that the enthusiasm of the musicians, or lack thereof, should not be taken as gospel.

What matters more than a conductor’s age, or any other factor, is whether the music director and players share a collective artistic vision and project mutual excitement. The Seattle Symphony has embraced the purposeful, adventurous leadership of the French-born Ludovic Morlot, 41, who took charge in 2011 after the 26-year tenure of the dedicated but uninspiring Gerard Schwarz. Both the players and audiences in Seattle were eager for a conductor to shake things up, as Mr. Morlot has. In parting ways with Mr. Gilbert, the Philharmonic has sent confused signals. Lately, he and his players have been on a roll, with two programs in New York that provocatively combined major premieres by John Adams and Thierry Escaich with exacting, vividly characterized accounts of Stravinsky’s “Petrushka” and Shostakovich’s 10th Symphony. The orchestra has just completed a successful European tour, winning praise for its playing and Mr. Gilbert’s programming.

It’s hard to imagine that the musicians are much clearer about the future they envision than the orchestra’s administration seems to be. They must have a say, of course. Still, go back to the coverage of the Philharmonic from the 1960s, and you can find players complaining about their conductor. His name was Leonard Bernstein.