I loved that scene. Sisko answering "in battle," was done with such force and the stricken look on Picard's face was priceless. I don't think an apology was necessary but perhaps implied in the sense that by the end of "Emissary" the healing process for Sisko had begun. I think the meeting with Picard really helped establish Sisko at a certain emotional place that would allow the arc to begin.
Sisko's reaction was normal to me. I mean, we didn't get to see enough of how the rest of Starfleet or the Federation might have reacted to Picard. I'm surprised that we didn't get an episode after "Home" where Picard has to fight to remain captain of the Enterprise. At least First Contact returned to the idea of people being leery about Picard in the event of a Borg incident.
It would've been great to see a Picard-Sisko team up in TNG Season 6. If they could've found a way to put Sisko into the "Descent" two-parter I probably would've liked it better. And I finally would've gotten to see Sisko v. Borg Round Two (even if it wasn't the actual Borg Collective).