Both manufacturers would probably say no, because of liability worries (e.g if the threads seemed compatible but you didn't get a good seal, leaked fuel, and started a fire - they think of worst case scenarios). The threads on many fuel bottles are the same, and in that case it should be compatible if both are (i) designed to be pressurised and (ii) have the same surface to accept a seal (probably just a flat for an O-ring)
However looking up the Soto, it's not the bottle you need, but the hose assembly that screws into it - the bottle cap if you like, and that's another matter. In many designs, such as my MSR, the hose comes out of the pump/cap assembly - quite possibly in both of these as well. This part needs to seal, so you need the same interface between the two. I can't see detailed pictures of them disassembled, let alone dimensioned drawings, but from photos there's a chance - and only a chance.
The Primus has a power regulator valve as well, so the Soto gives you the ability to run off gas canisters (butane/propane) as well as liquid fuels; the only real benefit the Primus offers for its higher price point is the lower weight, and you need to be sure to compare like with like (e.g. with/without bottle, which is a lot of the weight)