First off, congrats on the Bronco!!! Ford knocked out out of the park and my wife mentioned treating her CR-V in on one... I had a '68, '72 and '89 BII.
I think when the time comes, you can entertain both options. Main advantage of trading, at least for myself is it'll reduce the amount you'll be taxed on. Even though trade in will be lower, the tax savings could end up making it a wash selling private party.
However, dealer could low ball you bad enough that private sale makes since. When I went to buy my MKS, I was offered $1000 for my '02 Limited 4x4 V8 Explorer with 212k on it. I ended up selling it private party for $4300. I was able to put more down and cover the tax expense when that came due.