Bron is a man who isn’t willing to fight for (let alone die for) anything, and thus he has little to no understanding for anyone who is. Generally speaking he thinks everyone in the military is a more or less dumbass, regardless of the side. The Empire, to him, is just something bitter old men reminisce wistfully, a memory of “good old days”, bearing little resemblance to the post-war ruin where he grew up. So good riddance to them - no way he’d don a uniform and march to some pompous Legate’s tune for that broken thing. Stormcloaks he sees as a joke - a bunch of fanatics fighting windmills and actually thinking it will make things better. He sure mocks Skaila relentlessly for her conviction.
That said, it’s not like he has any better ideas as to how to run things. Bron is just the type of guy who sits on the sidelines, never risking his own neck, but sneering and sarcastically clapping at everyone else who does. If he really had to say which side he prefers, I think he’d find the Imperial Legion slightly less annoying. But only slightly. As far as Bron is concerned the Civil War can rage on as long as it pleases - chaos is good for his line of work anyway.