We know from the constitution of the Empire of Japan that the Emperor had nearly unlimited (theoretical) power; he was able to remove the Prime Minister as well as any members of the cabinet as he saw fit. I don't seem to be able to find the actual legal abilities of any of the princes, however, and from what I can tell even the Emperor's closest relatives drew their importance from positions they held that could easily have been held by commoners, not because of their 'blood'.
Princes of Empire were obliged as military officer but in there was not special right by blood in their service. They were also assigned seats in the House of Peers but no more than observer as custom.
In the Showa era two Prince was assigned in the highest post in the Military, Marshall Prince Kan-in as Chief of the General Staff of Army and Marshal Prince Fushimi as Chief of Navy General Staff. They were not only Prince, they had been recognized as talented officer.
Their authority as Prince and military career was so great that anyone couldn't oppose but it caused bad affect. in the Army conflicting generals competed his support and escalated conflict. In the Navy talented pacifist admirals were purged by Prince Fushimi's will.
Emperor Showa's three brothers were also assigned military officer. They often tried to advice but Emperor ignored. Because Emperor thought monarch must obey legal advice by the minister of government but advise by brothers were not by legitimate procedure. In addition Emperor didn't credit younger brothers because Prince Chichibu and Prince Takamatshu had once indicated sympathy to the social nationalism and Prince Mikasa was too young.