I think one potential of the PLC is the formality of it – if this group has a formal responsibility for students’ learning there should be a big incentive for focused collective learning that improves the students’ lot.
So, for example, if you thought about UK Heads of Department of economics across UK universities being part of a PLC, alongside others who teach and have an interest in teaching economics, then this could be a very powerful group in terms of taking teaching forward. Through the Heads of Department, learning could be disseminated and put into action. Presumably this could work similarly at University level, too.
As for the student voice? I think this would be part of the collective learning – being able to understand the student perspective and what makes for effective teaching is part of the journey to improving teaching.
So for me, CoPs still feel a little serendipitous, a more organic mushrooming of people with common interests if you like – PLCs, with a shared vision (which presumably would change and be refined over time) suggest the potential for a more focused drive to improve learning.