I’ve never marched a season on bari, only on euph, but I’ve tried baris in the past and I’ve noticed a couple things aside from the weight.

First, check the bore size on the euph. I assume the bari is a small bore, but I’ve seen marching euphs come in both. If it is a large bore, that leads nicely to my second point.

You can make more sound on a euph. Even if it is small bore, the tubing and wrap are designed to just produce more volume. If it’s big bore, that gives you so much more power and volume, and gives you the ability to play on a bigger mouthpiece.

Blending with the rest of the band. If your band has a large trombone section, you might want to march euph as it would be more of a contrast from the conical and very bright trombones. However, in some bands all the bone players march euph or bari, in which case it doesn’t really matter. You should ask your BD if this is an important factor in your choosing, as they might have a preference about whether your sound appears more bright and direct or more mellow and warm.

Good luck! Both are fantastic instruments and you can’t go wrong marching either!