Energy is the real difference in these 2 cartridges. If you look at full house load 10mm like it was intended they are not even in the same league. Most factory 10mm ammo is really light, and most factory .357 sig is really hot.
A G20 with 15+1 rounds and hits like a 41 Magnum is not bettered by anything other than a rifle.
10mm 180 grain at 1300f/sec or 675ft/lbs same as 41 mag.
155 grain at 1450f/sec or 733ft/lbs
357 sig 125 grain 1260f/sec or 520ft/lbs
(winchester load page on win's website)
That 155 grain 10mm load is just shy of a 44 mag load energy with a 200 grain bullet.(lightest for a 44 mag)
I am very partial to the 10mm, can you tell. I also have had a .357 sig and counldn't justify the price in ammo difference over a standard 40S&W. It is just a 40S&W necked down for lighter bullets. If I wanted a lighter bullet I'd shoot 9mm, they are cheap to shoot and I own a few of those.
Would I trust my life to a 9mm, no, I've been shot with one and I'm still here. 40S&W is the minimum I would bet my life on. Don't get me wrong, I like the .357 Sig, just not better than a 10mm. Oh yeah, the 10mm bites and barks harder than most auto handguns.
Look up the 1986 FBI shooting that prompted the developement of the ultimate handgun round, the 10mm. The only problem was the grip size and the recoil for smaller shooters. There hasn't been another round ever developed that proved better for personal defense. The developement of the 40S&W was just a smaller 10mm to reduce it's size and bite/bark.