Okay, after thinking on it, I think I'm coming down strongly on the side of Jack for Watch commander.
Ultimately, the Watch has been developed, at Van Hal's orders, as an organization primarily concerned with catching infiltrators. Now, we co-oped an organization that was nominally about keeping public order and maintaining legality of various things, but that's not what it's for. The purpose of the Watch is to fight shadow wars. To catch vampire spies, to give us information, to let us know when people are sneaking around and who is being suspicious. They do this by also protecting public order and being highly visible, so that they are trusted by people who then bring them more information and so that their overall moral goals keep the dedication to the cause among the ranks high.
But their job is ultimately not to fight off bandits and prevent thieves from acting. If there are bandits to be fought, they can let the army know and the army can go send some people to dispose of them. Their job is to help us detect spies and infiltrators, then deal with them. The guy who is a great intriguer type is simply going to build a Watch better at that job. The likely indication that he'll be setting us up to fight a war against the skaven is just a solid bonus on top of that. We don't need a leader whose ideas for the Watch involve building up a force who he can pull out of the cities to go and thrash some local beastmen in the forests- designing the Watch that way was an option during the Watch design vote and we didn't pick it for very solid reasons. The martial leader is more likely to build up the Watch into an organization of veterans who wish they were still in the military.
Yes, Jack's unlikely to ever want to quash the Thieves' Guild- betray those he's worked with, as he said. But that just means that we need to ensure that problems with theft never grow to the point where Van Hal feels it necessary to order us to quash it, not that we can't ever employ him because of a conflict of interest. Hell, we're a conflict of interest- we just all but openly told Jack that we worship Ranald and are doing this anyway, because it's true. If his job description includes keeping the thieves in line- not destroying them, but making sure that they won't overstep themselves- he'll still do that, which is all we need from him on that score. And we need his expertise heading up the Watch and teaching them what threats are actually threats- cultists, vampire agents, skaven- and what is just petty crime that yes, needs to be kept down, but is simply not as important.