Of the three you mentioned, by preference would be Odin, BA, Faxon.
I have one SS Odin barrel and it holds MOA with 5 shot groups. Buddy has a Faxon and it's more of an 1.5 MOA barrel. Keep in mind this is just two samples of one.
BA's owned by Aero, so it's considered a mid-tier value product. Several of the local builders use them receive few complains for the "normal" non-loonies like ourselves.
My goto is Criterion, but like everything else right now, they are in short supply.