everyone join PSP for respect, social recognition, power,serving country and unfortunately some for easy money as well.
Now on these basis we can compare both . an ASP has more social recognition and respect as compared to captain , The thing is that ASP deals with general public because ASP awam k kam aa skta hai, while Captain has only to do with army. The only reason people might respect Captain is because armed forces are considered to be prestigious .But that respect is only limited to the respect of army. while even if someone hates Police , he or she will still respect PSP officer because of obvious reasons .
again same is the case with power, ASP,SP etc have more powers . Powers of captain is limited to army personnel while that of PSP officer is spread in the whole city .
As with salary, I think there isn't much difference .
As with perks etc, as far as I know house an ASP or SP gets is much better than captain in most of the times, Captain doesn't have official vehicle and higher rank army officers might that but that is strictly for official use only while PSP has awesome vehicle .
I am not sure about security of Captain but PSP can get as much or as less guards as he wants. It depend on his nature.
As with serving country, I honestly believe PSP can serve much better . I have great respect for army and I agree that they are the defenders but think individually , captain can be replaced , and initial and replaced captain both would perform same duties . But an honest and dedicated PSP is bit Rare and can't be replaced easily.
Plus Police can easily earn black money while in army it is not possible until higher ranks,
and lastly one can only be promoted upto Major in army and promotion above it is dependent upon personal aptitude and service record but mostly PSP reach DIG at least .

P.S: these points are based on my personal research and opinion etc, I have no army,police background. One may disagree

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Somewhere Beyond Right and Wrong, There is a Garden. I'll meet you there :Rumi