I guess it all depends on your perspective. From my viewpoint I think police and firefighteres are held in HIGHER regard than the military. I am a retired Army office who served 24 years, still working in the health care industry. I find the most common reaction by people who find out that I served, and served for that long, is surprise, as in "I wonder why he stayed in the Army instead of finding a real job?". On the other hand, my youngest grown son was in law enforcement and when I told others about him there was universally positive comments made. Personally I respect and appreciate those who serve, both in the military and in civilian occupations where one willingly puts themself in harm's way to protect others. Thank you for your service in both realms. Don't be discouraged, there are many folks like me who are grateful to men like you who are holding the line against anarchy and barbarism every day.
The military is a separate world that few civilians ever see. People who didn't serve have no concept of what it is like to be a military officer. I was an E-4, but remember how hard officers had to work due to all the BS duties they were saddled with and the ridiculous regulations they had to follow.
It is a different world when civilians consider Public Safety workers. They have at least a small concept of what Public Safety has to endure due to TV reality shows, friends and relatives who work in the profession, and their interaction with said workers. In comparison, none of these circumstances exists when talking about military officers.
Having written all that, I don't know that Public Safety is held in higher regard than our military. During Vietnam, no one was held in high regard, but following Gulf War 1, our military's "stock" certainly climbed. Everybody likes a winner and our military certainly reduced one of the largest armies in the world to mob of crying little girls in record time. I can remember Bush the Elder making sure at least some guys got back to the US ASAP. The town I was living in at the time has a large parade each year in June to celebrate something and a local was served in the Sandbox with the 3rd AD standing in a Hummv. EVERYONE stood-up, clapped, and cheered as he rolled past. That would not have happened even 5-years before.
That stock climbed further after 9-11, climbed even more with Gulf War 2 and Afghanistan, the SEALS whacking those Somali pirates, and culminating in them introducing binLaden to the Mozambique Drill.