How do product managers and product marketers share the voice of the customer responsibilities?
PMs should always lead voice of the customer (VoC) programs
While PMMs need to have their ear close to the ground when it comes to customer feedback, it's ultimately the PM who will use the feedback to make product decisions. Additionally, PMs should never be in a situation where product feedback is "second-hand" or being prioritized by someone who doesn't own the roadmap.
I think "share" is the right term to use here. I've heard marketing teams claim that only they represent the voice of the customer, which is obviously not true. There are many groups in a company that interact with customers and listen to their voices. It's a PM's eternal challenge to figure out which voices are the ones they should weigh more heavily and which ones less!
I would say that PMs tend to engage deeply with a small proportion of the customer base and get a certain perspective that is then balanced by the views that PMM gains by interacting with the broader market using different instruments. For example, PMMs will gain particular viewpoints when they interact with analysts, or conduct win/loss analysis, that are often distinct from what PMs will hear from working with users. Good PMMs also tend to have a clearer view of the voice of the economic buyer in B2B software, as PMs tend to work with users more.
Lastly, I want to address the topic of customer feedback. Most successful companies tend to have some kind of customer feedback system where feature requests and other general feedback go. This kind of information is a goldmine representing the voice of the customer, provided there is someone -- usually a product operations function -- curating the data and summarizing common patterns for both PM and PMM. Without this, the feedback system is just noise and we lose the incredible valuable information buried in it.