Sure there may be more cops that became pilots, but I would also argue that a lot of pilots aren't cut out to be cops either. Hiring standards for LEO's is way harder than being a pilot. Background, physical, psych, written, oral and experience all play into getting hired. Then its onto the Captain's interview and an academy (6-10 months). It takes months, even years to get picked up at some agencies. Check out officer.com they have forums that are state specific and can answer more about the hiring process.
If you're at the bottom of a regional or lets say 5 years in and looking at a furlough or starting at the bottom again I'd say become a LEO. It really depends where you are in life. If your in your 20-30's you could do 20 years as an LEO and retire with a great pension. Go fly whenever you want without worrying about eating ramen nightly. You'd still have decades to go fly professionally after too.
In the end some people enjoy slinging gears, others enjoy gunslinging. Or better yet like someone said join the feds or local PD that has an aviation bureau and your set. Great pay, pension, and get to fly on someone else's dime.
Home everyday and a good QOL are something no amount of pay can make up for.