When we talk about the differences between something like an ideal-type feudal army and an ideal-type professional army, there are actually multiple factors that distinguish them from an economic, organizational and performance standpoint. Military forces can be full- or part-time; they can be paid and administered centrally or locally; they could be volunteers, mercenaries, conscripts or hereditary soldiers.

For a familiar example of a highly-professionalized army, let's look at the Roman army under the Principate (27 BC - 284 AD). Fixed commands were established at permanent encampments at strategic points across the empire. Soldiers received rations and cash salaries from the central government, and were devoted full-time to military service (whether training, fighting, or carrying out construction projects). Lastly, these soldiers were volunteers who entered a service contract in exchange for wages, occasional donatives and a retirement package.

For good examples of a feudal army, let's consider the Anglo-Saxon and Norman armies that fought at Hastings. Both were led by noblemen, with a solid core of well-armed household troops and the support of commoners called up for short-term service. There was no central administration for supplying or paying these armies, which would go back to their homes in peacetime and were fighting as a part of their social obligations, not as salaried work. The noblemen and their retainers were likely born into their positions as warriors; the commoners had been drafted.

Comparing the two, the ideal-type professional system has the advantage of allowing for large, well-trained forces to be kept in constant readiness, always available for a campaign; the downsides are the expense of supporting so many mouths not involved in productive work (agriculture or manufacturing) and the logistical challenges of feeding, paying, arming, training and manning such large armies at all times. Only a well-organized state ruling a prosperous realm can shoulder both the economic and administrative burdens of such a system. The feudal system dramatically cuts costs by keeping only a relatively small number of retainers or men-at-arms in constant military readiness, and having them paid and supplied by their local lord rather than by a central government. The highly-localized organization and structure is also better-suited to making fast responses to small, local threats (say, Viking raids) rather than long campaigns over great distances. Recruitment was also simplified by the fact that military service was an involuntary obligation, not a career choice.

In practice, many historical armies have fallen somewhere in between these two, trying to capture some of the advantages of both. In the Roman experience, both the Late Roman and Byzantine empires employed a mix of low-cost regional militias for local defense and elite, full-time professional soldiers for key battles. Medieval European states increasingly relied on taxes to pay for mercenaries or royal standing forces, rather than feudal levies. Chinese, Indian and Islamic traditions also had various mixed military systems throughout their histories.

To sum things up, a "bannermen" feudal military is relatively inexpensive, relatively easy to administer, and is effective for small-scale or short-term warfare. It suits weaker governments, less-developed economies, and defense against many small threats rather than a few serious ones. Professional armies are effective in combat and well-suited to extended campaigns against determined enemies; they are also complex and expensive. They suit rich, centralized states with ambitious military goals or dangerous rivals. But few examples from history conform totally to either ideal type, and instead try to mix different elements together to create military organizations that suit their unique situations.