Xenophon says that Jason of Pherae said no city state can easily contend with his 6k mercenaries, for though some can match him in numbers, the mercenaries are in their prime and always training while the same can't be said of what's essentially militia forces that make up the forces of usual city states.

Of course that's just his/Xenophon's opinion. Pherae was the strongest city in Thessaly, but did not perform so well when the other cities called in Thebes for help.

By mid-Medieval times, royal or 'national' armies were beginning to prefer professional soldiers over the feudal levy.

This is seen in the growing encouragement of cash payments instead of 'knights service' to fulfill the obligation of military service for land (earlier perhaps in England than elsewhere). The cash would then be used to hire professional soldiers. These were not necessarily 'mercenaries' (that is they were not often (at first) organized in mercenary companies that would hire their collective services to anyone who would pay). Mercenary companies became more common later in the Middle Ages.

Professional soldiers were not equipped any better than the feudal levy, and they did not necessarily have 'better' or different training, but they were experienced soldiers who sought out war (which was not always true of 'knights of the Shires') and they might well have trained more than country knights did. They also would campaign for as long as they were paid, whereas the feudal levy was usually only bound to serve for a limited time (40 days was a common term) and then might well go home (which didn't work very well if the English monarch was fighting a campaign in France).

There is probably an exception, where Genoese mercenary crossbow companies likely trained differently and were equipped better than other crossbowmen.

Crossbows were fairly common in mid to late Medieval warfare. Hunting crossbows were common. Most crossbowmen fought, however, as individuals, in castle and town defense and attack, and did not operate as companies or units in open field battle. The Genoese did.

The effective deployment of mass formations of crossbowmen in open field battle without the infliction of many 'friendly fire' casualties, must have required some form of training in 'drill' (somewhat similar to that required later by musket formations). In any event, if a medieval army wanted crossbowmen, they almost always hired Genoese mercenaries (or, occasionally, companies from Pisa), leading me to believe that they had developed specialist training and tactics.

The Genoese also had their crossbows made by the 'Ballistai' corporation in Genoa. (This manufactory is often cited, but not detailed in any sources I have found. Does anyone have more detail?), which may have been 'superior' (better for their cost - crossbows were generally quite expensive weapons) than crossbows made elsewhere.