NFMee, I guess your problem is solved, you're getting both.
If you had to choose only one or if you're still deciding on which to get first, I would recommend that you decide first how or where you will be using the knife most often. Then, I would recommend the Police if urban carrying is more frequent and the Military if backpacking is your primary use.
The Police is slim, sleek, and, imo, looks less threatening for EDC in the city than the Military. Also, I personally feel that the Police is more comfortable for EDC in my pocket. The Military's advantages for backpacking are its larger belly (for slicing foodstuff, etc. in the field), larger, ergonomic handle (for tough cutting/slicing/hacking), open back (for easier cleaning), and larger thumb hole (for use with gloves in cold environs). Although both knives are nearly identical in length, the Military's blade and handle are higher(?) and that makes the knife look larger than the Police. The non-knifeloving public could perceive the larger size as "more tactical" and "overkill" for city use.
I love 'em both and am glad I don't have to choose only one.