I just transitioned from an engineering role to a product management role. Product management means different things in different companies, but generally a product manager will interact directly with every other part of the company and "own" the product plan ---- what needs to get built and when. Engineering owns the how.

That said, I think project managers can really help things flow. If you've got a process you are sticking to, a project manager can help make sure things get done when they need to. This is especially important when lots of things are happening simultaneously (lots of clients and client requests, lots of business development effort, lots of growth, technical challenges).