Well Rawr I guess the main issue is that both groups have a completely lawful focus and people regularly expect them all to team up or fill in for the other when someone is not online. At a glance you could say that the LN and LPI fulfill the same role which is defense of Liberty. The Navy however is state funded and obviously militarized and has completely different goals and motivations... specifically open combat.
It is unfortunate that the LPI is almost always called in to deal with pirates, I really wish that police groups in general had more RP opportunities, since a Navy player can do almost everything the Police one can but with a bigger ZOI and better equipment... at least the cops get TLAGSNET, which is a minor step up, but with the activity in Liberty it must be impossible to use effeciantly. I think in the future police groups will end up getting more utility powers like shutting down trade lanes and mooring points, but that is just high hopes from me.
I sort of want to see a Liberty version of Law and Order now that I think about it, LPI officers doin' their thing XD