I’ve just had a paper published in J. Knot Theory and its Ramifications: ON THE Uq(osp(1|2n)) AND U-q(so(2n + 1)) UNCOLORED QUANTUM LINK INVARIANTS.
I wrote the paper for fun. It says (in part) that the two quantum link invariants mentioned in the title, where only the vector (smallest non-trivial) representation is used to colour all components of the link, are either identical or related by an abstract symmetry.
I proved the identical situation for one simple class of links – but suspect the invariants are identical for all links.
I’ll upload a copy of the paper as similar to the published version as possible when I have some time.