What does a product operations manager need to be exceptional at compared to a product manager?
I've found it's been critical to feel competent in running a business end-to-end. By this, I mean I've focused on taking a 360 view regardless of where I've sat within my organization (be it product or GTM). Every product needs buy-in across the entire village to make it successful- GTM, support, customer success, legal, partners, product / engineering, etc. Being great at communicating with and influencing engineers, for example, is a wonderful trait, but success comes out of one's ability to translate goals & requirements + drive consensus across departments.
The key tools I've consistently relied upon to help translate goals and build consensus / cross-department support are 1) a solid business model & 2) a resourcing plan. If, for example, a product team sets a certain revenue forecast without GTM owning the targets, support designating capacity, partners enablement, etc. it's a recipe for underachievement and conflict across teams.
Business models / resourcing plans pull teams together to agree on targets and prioritization. Surprisingly, I've found that more times than not, these key assets are either missing or incomplete, but it's absolutely worth the time to partner with finance to establish a great baseline that you can use to drive more productive and actionable conversations. The whole goal is to get all departments collaborating together to row the same boat in the same direction toward your product's success.
Lastly- I'd say it's critical to feel really comfortable being able to zoom out just as quickly as you can zoom in. This role requires that you can get your hands dirty in building processes and tools and running fault analysis (pretty much all the time), but I've seen too many people get stuck in the weeds at the cost of the bigger picture / vision / goals. Alternatively, I've also run into many examples where folks can stay too high level and big picture at the cost of timely execution. Walking the middle line can be challenging, but in my opinion, it's a very big part of being successful in the role.