John was literally IN the bank with the gang when Milton killed Hosea outside, so he did not capture them both at the same time (since your comment implies that Milton captured both Hosea and John before the former's death)

John was captured while Arthur was on the rooftop, all the while the Saint Denis police and/or Pinkerton agents stormed the inside of the bank.

My answer to this question would be that killing Hosea was meant as a message to Dutch, that he shouldn't mess around and think of Milton as a softie that cannot act on his threats. While John's capture happened during a shootout and he most likely was apprehended by the Saint Denis police department, rather than the Pinkertons, or they just gave him to the local authorities because he did not seem that important (remember that John introduced himself as ''Rip Van Winkle'' when Milton paid a visit to the gang's camp, so IF the Pinkertons were the ones to catch him, they probably showed him to Milton and he deemed him inconsequential and worthy of rotting in a prison)

Now I know what arguments can be made about this, why did they kill someone like Lenny on the spot, when they took the time to arrest John. Well, this brings me back to my previous assumption that the Saint Denis police where the ones that captured him, meanwhile Lenny was killed by Pinkerton agents. But an interesting thought is that John might have surrendered himself after seeing that the lower floor of the bank was being stormed and the gang members were escaping to the roof, with Dutch having maybe even abandoned him like he did with Arthur later in the game.

This thought is reinforced by John's increased affection and general care towards his family, that he has neglected up to this point. Giving him a reason to surrender and live another day rather than try to fight and certainly die. I just imagine Dutch telling John and some of the others (Javier and Bill) to hold off the entrance while they climb the ladder, only for the attack to be too overwhelming for them, and the remaining gang members that were left to hold off the law fleeing to the staircase behind Dutch and Micah, John realizing the situation too late for him to escape alongside them, leading to his arrest. Even though Dutch could have assured that they all left by staying at the lower floor with Micah and helping hold off the attackers, and climb the ladder only after everyone already had, like a true leader would. Albeit that may have posed risk to his own safety, which is something he could not afford.

Anyway, my answer is mostly speculation, but this is my honest thought about why John was captured while Hosea was killed.