The influence of politics on the Roman Army and vica versa

[The Stranger]

Basically the limitanei were "static" frontier garrisons - essentially local milita formations whose job was to deal with minor incursions and delay major ones. The comitanenses were conversely partly a developement of the old professional legions and partly local "big men's" private armies (to keep them safe from their political rivals and their armies natch - not that the old legions hadn't had this role too), full-time mobile forces that acted as a strategic reserve that reacted to problems the limitanei of threatened areas couldn't habdle by themselves and who also formed the backbone for foreign offensives.

so the comitatenses were basicly the forerunners of the later armies of the feudal lords. They were private armies of generals and such untill a foreign offensive came along and they were merged.

[Watchman]

Not really, by what I know of it. The feudal hosts were based on the personal retainers of landlords, often sub-feoffed minor landlords themselves, and only called to arms when necessary. The European version of the theme traces its ancestry mostly to the sworn household troops of Germanic kings and nobles.
The comitatenses were full-time professionals still to at least some degree paid by the central governement, even if they now in practice tended to answer to a local strongman when the push came to shove. It must be remembered that they were mobilized for foreign campaigns far from their normal base areas after all.

[Furious Mental]

As far as private armies, I think those were the so-called bucellarii