Composites Vs. Trading Groups

Does anyone know, in practice, if trading groups should exactly mimic composite groups?

I know they should be similar, but there are always restrictions for certain clients that will limit their ability to trade with a group. Is there a point when it would be prudent to permanently remove an account from a trading group but not a composite, or vice versa?

If anyone actually deals with these types of decisions in practice please let me know what factors could cause this.