So assuming you had a G23 which conversion would be better .357 sign or 9mm?
No question... 9mm.
Your G23 is already set up to shoot a nice defensive (high pressure) round. To me the only reason for a conversion would be to make it cheaper to shoot. Swapping to 9mm fills that bill. I'm not sure I would recommend carrying a gun with a conversion barrel in it. Most will say they may cause occasional malfunctions. While in training or non life threatening scenarios this is just fine, I wouldn't want a conversion barrel causing an issue when I need my gun to save my life.
Not to mention .357 sig is an expensive and hard to come by round.
Only downfall to the 9mm conversion is you will need to find some 9mm Glock magazines. The conversion barrel changes the chamber, but you can't feed 9mm bullets out of a 40 magazine. The .357 sig actually uses a .40 magazine because the round is built using a necked down 40 casing.