Nondenominational churches can be better than denominational ones since they may not be as tied in to doctrine, and a huge focus on doctrine. As an example, some Christians believe you must have full immersion baptism; others think it's a sprinkling. These types of small arguments can result in unnecessary debates. If a church is nondenominational, they may not be as adamant about things like this, and may be better able to absorb diversity. Still, they need to stand for something and have beliefs in line with mainstream Christianity in order to be good churches.
Nondenominational churches don't have a particular dogma they are trying to force upon its flock. These churches help preach tolerance and love above all else so everyone gets along. Nondenominational churches are wonderful examples of what churches should be because they aren't trying to win more followers over another Protestant sect.
No, nondenominational churches are not better than denominational ones, because there is no reason that a church cannot have specific beliefs. Denominatoinal churches are clear about the things that they believe and the things that they want other people to believe in and do. There should be variety of churches, because it is silly to fight over picky fine theology points.
This is one of those situations where there really is no standard concept of "better." Different people have different requirements for religion and spirituality. Some like the rules and structure of a denominational church, with all its history and pageantry. Some people don't need the theatrics to get closer to God.
Most people prefer to attend their own churches rather than non-denominational ones. Although non-denominational services are appropriate in some situations, most people do not want to attend that kind of a church all of the time. There is nothing wrong with having many different religions in a free country with freedom of religion.