Technically all kings were equal, but held rank according to the antiquity of their throne. However, France (which is the senior kingdom in Europe) and England (much less senior) both are more prestigious than other kingdoms --except the Empire-- because both sovereigns were anointed (given additional sanction by the Roman Church) during their coronation. The Holy Roman Empire was another matter, as it was technically the continuation of the Roman empire and superior to any other entity. But the Holy Roman Empire was also something of a joke, in that it had no unity, only a tenuous connection to Rome and was usually less than holy in its practices.
Coronations were not necessary to install a king. Even before he was crowned, the king was the king. The heir to the throne automatically became king the instant the former king expired. Thus the ancient cry, "the king is dead, long live the king." But a coronation was a public ceremony which pinned the new king down to various campaign promises and the like. During a coronation there was a lot of swearing of oaths by the coronee, and there were a plenitutde of witnesses.
During a coronation in France (which technically had to take place in the catedral at Reims), one would have to invoke the Trinity, the Virgin & Joseph, St. Denis (patron of France), St. Martial (of the French in arms), and St. Genevive (of Paris).
For England Westminster Abbey was the traditional place for coronations, durnig which St. George and St Michael would be invoked.