This is a really complex question, and I can't give any kind of comprehensive answer. Some thoughts you mind find relevant:

• It isn't too difficult to learn the basics of economics, and doing so will give you many more options as a scholar in the future (whatever field you end up in). While you didn't mention wanting to get a PhD, I think some of 80,000 Hours' thoughts on the benefits of an econ PhD could still apply here.
• I'd be surprised if there were many jobs that would accept you if you had a degree in Environmental Policy, but not if you had one in Environmental Economics (or vice-versa). I'd expect these fields to overlap enough that you could use either one as a springboard to a job (as long as you know what kinds of jobs you want in advance, and choose your classes/research areas accordingly).
• If you're looking for an especially high-impact research position, at an organization whose work/influence is very strong, I think it's especially likely that the strength of your CV/application will matter much more than the Master's program you select (my impression is that effective organizations tend to care more about skills than credentials, relative to less-effective organizations).
• As an example, Hauke Hillebrandt has a PhD in neuroscience, but he is among the most influential members of the EA community as far as promoting climate change as a cause area. (This recent article about his work got a lot of attention.)
• You could also look at the organizations the Open Philanthropy Project has funded to work on climate change, or those they cite in their write-ups on the topic (pretty easy to find if you use their Grants database or Google terms like "Open Phil climate change"). I'd guess that the people working at those organizations come from many different environmental-science backgrounds (or even unrelated backgrounds).
• All in all, I'd recommend choosing the combination of school/program that seems best for you based on whatever variables you care about, including "location" and "cost". Going to a more prestigious school with access to better internships, getting a good scholarship so that money isn't a concern, being in a physical environment you enjoy... all these factors seem like they would more than make up for any differences between the two types of programs you're looking at.