I've had the thought that, since both are essentially Hornblower knockoffs in space, the David Weber is going to eventually have them encounter each other, although Kirk, of course, will have to be literarily disguised. Since the Solarian League reads as a darker version of the UFP, he'll be a Solarian Navy captain.
So, just for fun, how would you see such an encounter?
1. What point in their respective careers?
2. Do you prefer cross-over encounters or in-universe counterpart encounters? Would it be better to have the 1701 (No bloody letters) pop out of the wormhole junction, or for Honor to get her ass kicked by a Solarian captain with all the tech disadvantages they have compared to manticore, relying on Kirk's famous luck, bluff, and supposed tactical acumen to beat the Salamander when all the bookies are saying the Sollies are toast?
On the flip side, Honor popping up in Trek could also be interesting, whether her fleet winks in from an astronomical phenomenon, or she's an exhange officer from the minor human polity of Manticore, outside UFP space.
This could be "his/her counterpart has always been in that world", "Q snapped his fingers", or whatever rationale you want, but if you were to write this, how would you do it?