Transactional leadership and transformational leadership are both effective forms of leadership. Some people might prefer using one over the other, and some employees might prefer to have one management style over another, but both types of leadership are capable of motivating employees, students, athletes, etc. to work hard and get the job done. A key difference is in how each leadership style motivates those people.
Transactional leaders often are not looking to change much of the daily operations or structure. If things are working and going well, this leader doesn't want to disrupt that flow. The main way that a transactional leader motivates people is through strict control and effectively using punishments and rewards. Subordinates are rewarded or punished based on performance. This type of leader generally has a strong personality, is focused on goals, and tends to be reactive in nature. He or she won't make a change unless something is performing poorly.
Transformational leaders are on the other end of the leadership spectrum. They aren't better or worse leaders. They simply motivate differently. Transformational leaders are more focused on inspiring subordinates to follow their leader. The transformational leader tends to be more proactive in nature and will go beyond only managing the day-to-day operations of the classroom, team, company, etc. This leader focuses on team-building and seeks to empower those employees and give them opportunities to be self-motivated and perform well for sake of performing well. The transformational leadership style only works well if the leader is inspiring and charismatic to begin with. If they are not, their subordinates are not inspired to be better, and a transactional leadership style should be incorporated.