In liturgical churches (Catholics, Orthodox, Anglicans/Episcopalians, Lutherans, and others), the clergy almost always wear vestments (liturgical garments) during church services. In Western churches, the vestment usually includes the Cassock (a long robe), the Alb (a garment worn over the Cassock) or the Cassock-Alb (a more modern combination of the two garments), and a Pectoral Cross. Depending on the tradition, a number of other garments are worn. In Eastern Churches, a whole other set of garments with other names are worn. Each garment has a special significance, and an extensive study can be undertaken to understand the significance and relationship of all the garments worn by different traditions. Vestments tend to be colorful and often come in many different colors. I visited several churches where the clergy wore vestments.
In history, many (not all) Protestant churches (especially Congregational, Presbyterian, and Reformed) gave up colorful vestments in favor of black preaching gowns - which look somewhat similar to a judge's robes. The general idea was to simplify the vestments and to reflect a more sober and somber view of delivering God's words. (However, some preaching gowns have color.) I did not visit any churches where the minister still wears a black preaching gown (though some had pictures of clergy who did in the early days of their church). In some churches, the minister wore a preaching gown (or robe) with colors. It might be fun someday to visit a church that still observes the wearing of a black preaching gown.
At some point, Methodists clergy in England began wearing business suits (often with a collar). Over time, many clergy in non-liturgical churches have taken to wearing business suits during church services (and in many churches this is a requirement or simply expected). The idea is to reflect what a serious person would wear in the surrounding culture. I visited a number of churches where the pastor wore a business suit.
In churches that follow a more contemporary type of service, the pastor is given the freedom to come dressed in casual clothes - and sometimes they are dressed more casually than the congregants. The general idea is that through faith in Christ, God is approachable and we can feel comfortable in his presence. I visited several churches where the pastor wore casual attire.
Now many believers often have strong feelings or beliefs about how the clergy should be dressed, though Scripture has little to say on this point. (Scripture did have much to say about how the priests in the Old Testament were to dress.) Then again, many have strong feelings or beliefs about how others should dress in certain situations. There is an interesting mix of customs, traditions, feelings, and freedoms about how we dress and how we dress in certain situations. I tend to believe there is a great deal of freedom in this area as well as freedom for churches to set certain standards for their clergy to dress during church services. I want to enjoy the rich diversity here rather than try to decide exactly which is correct here.