Hi!

Since you are interested in the privileges of Brandenburg and Bohemia, thankfully most of these official privileges were enshrined in the 1356 Golden Bull which provided the de jure constitutional backbone of the Holy Roman Empire until its dissolution.

For the position of Margraviate of Brandenburg, aside from the common rights and privileges of the Prince Electors such as including but not limited to the Privilegium de Non Appellando which I explained here, the right to mint money in their own states, and such, there were certain ceremonial duties they have to do, especially during assemblies, as enshrined in Article 4 of the Golden Bull;

We decree, moreover, that, as often as an imperial court shall henceforth chance to be held, in every assembly,-in council... on the left side, immediately after whichever of the aforesaid archbishops shall happen to sit on the left, the duke of Saxony shall have the first, and, after him, the Margrave of Brandenburg the second place. [1]

"Moreover, when an imperial court is held, the Margrave of Brandenburg shall present the water for washing the hands of the emperor or king of the Romans." [1]

Brandenburg actually got the short stick of the bunch since in the Letters of Intimation (art. 18), the Golden Bull states that;

"... notwithstanding your or your envoys' absence, we, together with our other co-princes and co-electors, shall take final measures in the aforesaid matters, according as the authority of those same laws has sanctioned." [1]

Which means that theoretically, any council of the Prince and Ecclesiastical Electors can start, decide and end without the Margrave of Brandenburg's participation.

With their privileges, I suppose that legally, Brandenburg's status not just as a Margraviate but also as an elector of the HRE, they were allowed to request Imperial Bans on their rivals and enemies. An Imperial Ban or a Reichsacht, preserved intact in the Golden Bull from the Sicilian constitutional reform all the way back from Frederick II Hohenstaufen [2] is essentially a command decided upon either by the Electors Secular (Brandenburg, Bohemia, Saxony and the Count Palatinate) or by the Holy Roman Emperor stripping a certain entity (a common person, counts, dukes and even the King of Bohemia at one time) of their lands, titles, positions and other possessions within the legal framework of the Holy Roman Empire, and thus allowing any other member of the empire to attack these entities to enforce said ban. This is exactly what happened to the ruling house of Pomerania-Stettin when it came into conflict with Brandeburg under Frederick I von Hohenzollern. [3]

Additionally, Brandenburg, together with the other three Electors Secular (except Bohemia) had the benefit of mandated Primogeniture succession under art. 25, which exempted them from the fracturing of titles under the (personally, I call it cursed) Partible Inheritance which weakened several states such as the duchy of Bavaria in the 1200s when Otto II of Bavaria’s land was shared amongst his 3 sons upon his death. [1]

Bohemia, meanwhile, had additional privileges enshrined in the 1356 Golden Bull such as exclusive rights over mining without having to share any revenues to the Emperor as stated in art. 9;

“We establish… that our successors the kings of Bohemia… may justly hold and lawfully possess- with all their rights without exception… all the gold and silver mines and mines of tin, copper, lead, iron and any other kind of metal, and also of salt: the king, those which have been found, and which shall at any future time be found, in the aforesaid kingdom and the lands and dependencies of that kingdom,-and the aforesaid electors in their principalities, lands, domains and dependencies. And they may also have the Jew taxes and enjoy the tolls which have been decreed and assigned to them in the past, and whatever our progenitors the kings of Bohemia of blessed memory, and these same prince electors and their progenitors and predecessors shall have legally possessed until now; as is known to have been observed by ancient custom, laudable and approved, and sanctioned by the lapse of a very long period of time. [1]

And they also have their own succession law as enshrined in art. 7;

“...Saving always the privileges, rights and customs of our kingdom of Bohemia concerning the election, through its subjects, of a king in case of a vacancy. For they have the right of electing the king of Bohemia; such election to be made according to the contents of those privileges obtained from the illustrious emperors or kings of the Romans, and according to long observed custom; to which privileges we wish to do no violence by an imperial edict of this kind. On the contrary we decree that, now and in all future time, they shall have undoubted power and validity as to all their import and as to their form.” [1]

SOURCES:

[1] The Golden Bull of 1356; Translated and Scanned by The Avalon Project of Yale University (Link: https://avalon.law.yale.edu/medieval/golden.asp) [2] Contrary Commonwealth: The Theme of Exile in Medieval and Renaissance Italy by Randolph Starn [3] Brandenburgische Geschichte by Inigo Materna, Wolfgang Ribbe and Kurt Adamy