The quality of the mesh is important, you have to take it into account, but when you can't do otherwise than using a bad mesh, a modifier to add under the armature modifier of the costumes is the smooth corrective modifier which often works wonders when the geometry of the costume does not have the quality of the character geometry.

Avoid having two or more armature modifiers on the character mesh, it can happen during various operations, removing the one that is in excess or unnecessary often fixes things, and this for all EBBAWT tools. Moreover a costume cannot have an armature modifier before using fit to active... because fit to active adds an armature modifier.