The .357 Sig will penetrate more barrier material but with the same ammo, on human opponents, will expand and stop inside them.
The bullets are designed to do just that and work quite well.
As for more flash and blast, hey all high powered handguns have flash and blast, be it 9mm, .40 S&W, .357 Sig, .45 ACP, .357 magnum...
But as for flash, most high end ammo has flash retardant power.
Table 3. CENTERFIRE PISTOL DATA
.25 ACP 155.0 dB
.32 LONG 152.4 dB
.32 ACP 153.5 dB
.380 157.7 dB
9mm 159.8 dB
.38 S&W 153.5 dB
.38 Spl 156.3 dB
.357 Magnum 164.3 dB
.41 Magnum 163.2 dB
.44 Spl 155.9 dB
.45 ACP 157.0 dB
.45 COLT 154.7 dB
.357 Sig ought to be near the .357 magnum but I doubt more cause there is no flash gap on semi-autos.
But also note the 30-06 in the other table as well as the 12 gauge in 18 inch barrel form.
GIs's shot lots of 06 in WW2 and Korea, and 7.62 Nato since then. I doubt any loss of hearing from firing a few shots in SD.