Assuming you have a degree, the LE experience may give you a slight edge over military experience. Many candidates will have all 3 (degree, mil & LE). The key is to try and make yourself as marketable as possible. No matter which you choose, (LE v. military), there are things you can do to make yoruself a better candidate.
Specific MOSes in the military are not all that important (unless you can get certified as an 1811 in the military).
I can tell you one thing, contrary to what recruitors tell you, being an MP will not give you an edge into getting into civilian LE.
We bring evil things to evil people, kicking in a door near you!
."In theory, there is no difference between theory and practice. But,
in practice, there is."
- Jan L.A. van de Snepscheut
"The difference between 'involvement' and 'commitment' is like
an eggs-and-ham breakfast: the chicken was 'involved' - the pig
was'committed'."
-unknown
Working on a PhD in CQB one doorway at a time.
When the wolf attacks, he will find not all who run with the flock are sheep!