I think it turns on the fact that the Armed Forces are self-selecting, the wish to serve your country being a very big factor.
I imagine there's a fair bit of selflessness in the emergency services. For instance I've only known a few coppers but they all were really motivated by trying to stamp on the bad b**tards for the greater good of all.
I suspect that the real problem with the emergency services is one of questionable leadership combined with unions. Senior police officers make me despair. They all seem to be very slick modern management types and I presume it is they who set an agenda which has coppers wasting their time bothering about postings on the internet as opposed to feeling collars. The big advantage which army commanders enjoy - apart from the self-selecting nature of the troops - is that the whole organisation can and even wants to keep a bit of distance from wider society and its attitudes.
My final moan, as an ex-soldier, is the devaluation of the word "hero". By definition, the fewest of us in any walk of life and that includes the armed forces, are heroes. The vast majority of us are average. So I don't accept that all members of the emergency services are heroes and to see that maintained makes me cringe a bit. (This morning I heard supermarket till operators being described as heroes.) What they are however, are people doing a valuable job which at the moment we are appreciating the full worth of. Some of them appear to be underpaid. Are they worth more than bank managers, TV presenters and professional sports types? Probably IMO. Are NHS managers and Chief Constables worth their pay packets? They probably get paid too much IMO.