I own a Military and a G-10 Police. My Police is in the original grind, not the flat grind, but I think I can speculate on that.
The Military is a large knife. Yeah, any 3 3/4"-bladed folder is large, but it's a real beast. I don't mind, but it puts some folks off. The blade has a deep belly (curved portion before the tip), and a full flat grind over its substantial width. This gives it excellent cutting geometry and a remarkably thin tip, despite the beefy 5/32" blade stock. The 440V blade steel is by most accounts the best stainless currently used in production folders. The handle is oversized for use with gloves (as is the blade hole) but is quite comfortable to bare hands as well. It supports a very nice "choked up" grip for cutting precisely with the deep belly. The "hump" is grooved for secure thumb purchase, but I found these grooves snagged my pocket on the draw, so I recently made some minor changes with a Dremel tool. The linerlock is rock solid; gives the knife smooth, light action; and is recessed in a way that I have never come close to disengaging it by accident. The clip is large and shiny.
The G-10 Police model is a very light knife at only 3.4oz. It is large, with a blade that most would call 4 1/4", but still smaller overall than the Military. The blade is narrow with a long, straight edge. This lack of belly may be an advantage for seatbelt-cutting, but is less suited to general utility. It also has a very fine point. I have been very impressed with ATS-55, which seems to offer ATS-34's good edge-holding, while being less brittle and easier to sharpen. The handle supports mainly one grip, an excellent saber-grip, but you cannot choke up and even with the G-10's added security, slipping onto the edge might be a problem should a thrust strike a hard object. I have no problem with my thumb slipping off of the ungrooved "hump," which is also lower-profile on draw than the Military's. I have very rarely snagged the large protruding locking notch while drawing the knife. The lock on my knife is solid and so stiff that "dropping" the light handle open is difficult. The clip is black.
The Military offers a better utility blade shape, better steel, more grip options, and is useable with gloves on. Its linerlock makes it easy to open with the "drop" method, but there are always a few folks out there who seem to be able to disengage these with a tight grip.
The G-10 Police is lighter and smaller overall. It has a smoother draw due to its un-grooved hump. Its lockback design is harder to "drop" open, but perhaps less likely to accidentally disengage. Its clip is lower-profile.
Personally, I have never accidentally disengaged a linerlock and would choose the Military in a heartbeat. In fact, I do choose every morning, and I usually choose the Military these days.
Little Bear Knives