system
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human
[ST:TNG] Two questions about captaincy.

In the episode, Redemption II, when Data captains the Sutherland, he clashes with his first officer when that officer starts giving orders without Data's consent or approval. Data reprimands him, calling this inappropriate.

On the Enterprise, though, Riker does this all the time. Was Data wrong, or does Picard use his captain's privilege to grant Riker more slack?

In the episode "The Wounded", Picard is hunting down a rogue starship captain who is risking war by violating a treaty between the Federation and the Cardassians. When Picard finally catches up with him, he gives him orders to follow the Enterprise back to Federation space. Picard also says that he will allow the other captain the dignity of maintaining his command for the duration fo the journey. If the captain refuses the orders, he will be placed in the brig.

On the face of it, they're both starship captains, so they're both of equal rank. What gives Picard the authority to give orders to someone of equal rank? He has orders from Starfleet to deal with this situation, but is that the beginning and the end of it, or does he also have higher standing over other captains for commanding the flagship?
gpt
When it comes to two starships and two captains of equal rank, Starfleet protocol gives command authority to the captain of the more tactically-superior vessel. (this is said in the Voyager episode "Equinox") In that particular case, and probably any case involving the Enterprise-D at the time, Picard's authority was the dominant one. Plus, with the Enterprise being the flagship and a dominant status symbol for the Federation Starfleet, his decisions are still on top. Even Admirals defer to his judgment at times.

For the other one, there is definitely a certain rapport between Picard and Riker that allows the two of them to show minor disagreements while on the bridge. But that was built up over several years, and they showed on multiple occasions that their differing viewpoints were critical to solving problems. It's technically against regulation for that to happen, but ships out in the vastness of space can't always rely on strict interpretations of the rules if they wish to survive. 

However, their professional relationship doesn't really descend into the levels of pure insubordination that Hobson showed to Data. Riker will still defer to Picard if the captain finds something objectionable, and he won't argue the point until they're in private. Hobson showed blatantly racist and disrespectful behavior while harboring a frankly punishable attitude in the middle of a crisis. Any of the other captains we know about would have removed him from the bridge at the very least, if not confined him to quarters for the duration of the mission.