Uh, none of the above? I'm not in the majority about this, but think there are plenty of better choices for trees and soft snow therein. Chutes, another story. I've owned Cochises, very stabile in steep terrain, decently quick. They'd work for chutes.
Barons, yes you'd be crazy. Both skis are comparatively heavy. Why would you want to skin with them? And if you don't actually skin, why put on Barons?
Other things to think about: Trees like a supple and fairly moderate flexing ski. If you want something fat, the Patron or Soul/Super 7 come to mind. Chutes are no fall zones, usually, so you want something that's quick to come around, easy to horse into jump and retraction turns, but stabile at the speeds that will come once you're down a ways. Personally, I think the Stockli Stormriders or the Fischer Rangers fit that bill, but the Bonafide IMO might work well. Only problem would be that at your size, it'll be borderline stiff at 180, but at 173, may offer fore-aft COM challenges at speed. And again, odd choice for a Baron.
If you want to skin a bit, using AT, then weight is a real issue. Yeah, I know there will be folks here who swear by their SteelRail 2000's, which weight in at 6,000 gm and any Real Man can enjoy running uphill on them. But for the rest of us skis under 3800 gm, ideally under 3600, are about right.