Pros
Zynga gives lots of autonomy to product managers - you really do lead the direction for the product! The nature of their product allows for really quick data analysis and ability to apply those learnings with new features very quickly. You'll be able to go from idea to release of features in days or weeks, not months. Numbers make people accountable: it will be clear whether you're features are doing well or not and why.
Cons
Focus on metrics can be a bit myopic at times... to the detriment of things that are hard to quantify like "fun" for users. Long term sometimes suffers at expense of short term With power comes responsibility and sometimes long work hours (certainly with stress if/when your product isn't doing as well as expected)