In my experience, Bullseye works well for both 9MM and .357 Sig. I’ve had my best luck using Bullseye and Win 231 for 9MM and AA#9 for the .357 Sig.
When loading longer bullets like the Lehigh Defense 125 gr copper bullets in .357 Sig however, I had to use faster powders in order to seat the longer bullets properly. I like Bullseye and Power Pistol for this application but Power Pistol produces quite a bit of flash in the .357 Sig round.
I tried Power Pistol in my 9MM loads but had better accuracy using Win 231 or Bullseye.
If I were to pick one powder for both cartridges, it would be Bullseye.