This is an interesting topic. I had a strong interest in becoming a cop shortly after college, but without any prior military experience, my degree was pretty much worthless. I discovered that the military was a better fit to scratch that itch for adventure (because for me, I primarily wanted an adventurous job), so I began to focus on my military career and I've been trying to find a full time Guard job for years.
Lately though, since budget cuts have made that goal increasingly difficult, I've considered law enforcement again, though now, 13 years later, my idea of the kind of job I'd want is quite different. The concept of a peace officer, idealistic or not, is more appealing. I don't want to arrest people for small amounts of marijuana, for example, and I loathe the idea of pulling people over for minor safety violations, especially to fish for another offense. So unless I found exactly the right department, I might not be a cop for very long.
I'm also pretty firmly turned off by the militarization of police. I was in the Infantry, I don't need that kind of environment while protecting the public. I'd like a carbine in my cruiser but that's about the extent of it. I also don't think I should have to attend a full academy; just teach me the laws I may need to enforce, how to work a taser, and how to drive like a stud and I'll be good. I already have OC spray, baton, firearms, I'm already in good physical condition, and I'm already disciplined. At 36 years old, I don't need to be broken down and rebuilt as a new man. The Army already did that once.
Since I doubt I'll ever find a job like that, I'll just stick with the Guard. Better to stick with an eight-year career and go full time with it than start over entirely. Though the job I've described does sound appealing, it may only be a fantasy.