In hiring additional Product Marketing Managers, is it more important that they have Product Marketing experience, or that they're a well-rounded marketer/communicator?

That depends on what you are hiring for and the level of experience you need in the new hire. If I were to hire someone to run my competitive program, for example, I would look for a PMM that has done this in the past, has created a competitive program from scratch and can show me examples of the battle cards they've created and the impact they have generated. 

If, on the other hand, I need someone to support an existing program and I have someone more senior that is overseeing the program from a strategic perspective I can look more for someone with a different set of experiences but that has a knack for details, that can to research and analyze data, and can learn on the job. 

A well-rounded marketer/communicator can be a great asset for a PMM team if you need someone with those specific skills. I think it all goes back to what your key priorities are, how you will be supporting the business, and the skills you need in your team. 

This depends on where you are in building your org, and your own experience. My path to PMM is that of a career generalist. I started my career as an engineer, then a sales engineer, then made my way to product management and marketing. I then took a left turn into consulting services before returning to product marketing. If I have a small team I will favor PMMs with some experience, but as I scale I like bringing in other perspectives and experiences into the organization. 

Strong communication skills are a must regardless of your background. Hard to be successful as a product marketer without strong communication skills.

I've really come to value true product marketing experience in my more senior hires. It's really nice to have a few folks on the team who know the drill. But I've also found that my PMM teams tend to skew more senior overall, each person is sort of in charge of an area and as such you want a more senior person to lead that. Which means that the career path to PMM is often building up experience in other roles and transitioning into PMM later in the career, so for mid level roles I think that well-rounded marketer could be a perfect fit.

Product Marketing means different things in different companies. So, asking for "prior PMM experience" may not always be as helpful as you think since this experience could mean something completely different from what you are looking for. While relevant PMM experience is a plus, I have also hired several people from non-PMM backgrounds into PMM roles. Specifically for tech, people who have spent time in customer-facing roles (especially those with a technical element) tend to ramp well in PMM roles. Some examples are Customer Success, Solutions Architect/Engineers, Technical Evangelism, etc. I myself am a convert from Product Management to Product Marketing.

I usually find the following traits helpful in identifying PMM candidates:

• Ability and willingness to understand the space, i.e., the product, the target customers, the usage scenarios, the competition, etc. Even if a PMM is not a domain expert to begin with, I expect them to intentionally build the right level of depth over time. In my opinion, this is what allows them to produce differentiated output.
• An appreciation and understanding (even if not expertise) of other marketing disciplines like DemandGen, Content Marketing, Comms/PR, Lifecycle Marketing, Field Marketing, etc. What PMMs produce informs (or should inform) what these other teams deliver to customers/prospects. So, understanding their craft helps PMMs do their jobs better.
• Ability to articulate product (and company) value proposition in terms of what customers care about. I put heavy emphasis on writing. PMMs should be able to tell stories both internally (about customers) and externally (about products and solutions) 
• Collaboration: PMM, by definition, is required to be a highly collaborative role sitting at the intersection of Product, Sales, and Marketing. 

This really depends on your current PMM team, and how they are structured. 

• If you have PMMs that are very specialized in certain areas and are you trying to grow the team, think about what gaps you have and focus on that in your hiring process.
• If your team is full of marketing generalists that are doing a little bit of everything, then again, identify the gaps - are you missing specific PMM skills on your team? then focus on hiring for that.
• This also depends on the level of seniority you are trying to hire for. If you are hiring junior PMMs, and are willing and able to mentor and train them, then look for someone more well-rounded! If you are looking for someone more senior who can come in and just jump into taking over and driving projects, then you probably want someone with more experience specifically as a PMM.

Overall, I think looking for someone more well-rounded is always a good idea because things change often and In my experience, the structure of the PMM team can also evolve over time, so I try to find people that can evolve with the company and change roles if needed.

I wouldn't under estimate solid PMM expierence, but I wouldn't let lack of direct PMM experience be a blocker either. As you've calledo out, being a well-rounded marketer/communicator is really important. My perspective is, if someone can demonstrate they are a solid story-teller - can take product and technical messages and translate them into customer value, this usually sits at the heart of PMM skillsets. This skill is so important in being able to support GTM stakeholders. 

I'd also spend time understanding how candidates problem solve. Do they start with identifying the problem, or are they looking to jump straight into solutions. This will help define what kind of partner this person would be to their product counterparts. 

With a solid interview and take home assignment, these are usually skills that can be detected quickly. 

The answer depends on the stage of your business and the depth of your marketing bench. As one of my mentors shared with me: As you get started, you need a good pool of generalists who can do the job you hired them for—and potentially cover off short term needs that may fall out of their explicitly-defined scope. As your team grows, you should start to become more aware of some of your greatest marketing opportunities, and can hire specialists for those roles. 

Just remember: Someone had to give every PMM you know a shot at the role before they had formal experience.