According to the principle of primogeniture, the most exclusive status would be the line of descent of firstborn males. At each generation, any father can only have (at most) one eldest son. Unlike all other forms of royal descent, there is no exponential increase in the number of eldest sons over aeons of time. Thus, primogeniture tends to keep a kingdom or dukedom whole. There is (at most) one legitimate claimant to the throne. Of course if there is no eldest son, the rule of primogeniture leads to the foundation of a new dynasty, with possibilities for attendant chaos.
In cases where rule over a major chunk of real estate has been at stake, the determination of inheritance would seem to be a matter of considerable social and historical importance. In traditional kingdoms, the divine right of the royal family was mostly unquestioned, with the possible exception of a small riff-raff of ne'er-do-wells. And there wasn't much alternative to taking the elder King and Queen's word for it, when it came to the legitimacy of a Prince's claim to the family inheritance. So the question "mattered" to just about everyone in the kingdom, as well as all the historians and court reporters. And we see a broad historical consensus about questions of royal descent, at least in many cases. It wasn't just a matter of the royal family's private record-keeping.
There are, of course, many situations where the nature of royal descent is more ambiguous, and the consequences are less obviously important. Who cares about even the first-line male descendant of a King whose Kingdom has become a Democratic Republic, or conquered by a neighboring Kingdom? What is the importance of being a descendent of Charlemagne's seventh daughter, or one of Attilla the Hun's concubines? Hmm... if you're inclined to believe that royal persons have favorable genetics (greater strength, intelligence or beauty) or for that matter, unfavorable genetics (psychopathic tendencies), then any royal descendant might have those genetically inherited properties, to some greater or lesser extent. Growing up in any royal family is likely to provide certain "perks" such as education and access to resources, which could make the beneficiary more likely to become a high achiever and thus a contributor to the family fortune. And the personal attributes of royalty could "matter" on a social basis, again boosting the fortunes of anyone fortunate enough to be affiliated with the royal family. These benefits could persist for many generations, or indefinitely, even after the loss of the actual earthly Kingdom.
As a matter of fact, it seems that royal families kept control of the Church by sending their second sons into the priesthood, to become the Popes and Bishops.
By all appearances, now that we are into the third century since the French and American revolutions, the power of the ancient royal families is severely in decline. Upstart businessmen and politicians and media personalities appear to be very powerful, while the antics of Prince such as Charles, Andrew, William and Harry seem to be nothing more than a circus side-show.
Richard always argued that appearances were deceptive, and that the European royals are in fact far more important than they appear to be, even into the present day.
Seeker, are you inclined to agree with Richard about this? I never felt that he presented a convincing case.