Having 2 HK45's and 3 HK45c's I can tell you that I like the HK45 more than the HK45c. Despite the number of guns I own, I plan on more HK45's, and no more than 1 more HK45CT. The grip texture on the HK45c is too smooth for me. The HK45 is perfect. I would also go with the HK45 for these reasons as I am also in LE.
1. You want a very solid grip on your pistol. The texture on the grip of the HK45 is perfect for all conditions. Wet, dry, hot, cold, and bloody. Something you have to seriously consider as a member of Law Enforcement. You may get into a gun fight(You may have already been in a few).
2. Full size guns are better for accuracy and speed. If you have to engage quickly, or make a clean shot, you will want that 6.61 sight radius. Also, with the tactical, you get the meprolight night sights with the ledge for 1 handed manipulation. (Also on the HK45CT.)
3. The magazine release deck is larger on the HK45 vs the HK45c. It may not be much, but it will count if you are losing your fine motor function because of cold, or stress.