Just an idea I had:
The Jedi aren’t a monolithic entity, like any religion (I know they aren’t really one, but bear with me) there are different sects, with most of them being considered “the Jedi”. The sect that Yoda is closest to stress pacifism (wars not make one great), so they usually reject lightsabers (preferring to use nonviolent and the force), and tend to include those with greater force abilities. The other sects are closer to the PT Jedi (without the “no marriage” rule), with some believing the Jedi should take a more active role in running the galaxy. Most Jedi usually stay with their teacher’s group, but Ben, being something of a maverick, leaves Yoda’s sect to join the more proactive Jedi.