I did a search for mechanical properties of 17-4 PH stainless steel. The data is a little difficult to correlate. I was particularly looking for low temperature impact properties. The only charpy v-notch values I could find for the solution annealed condition were at room temperature. Different companies supply the material in different heat treat conditions. It appears to me that for our purposes, the H-1025 or H-1075 condition would be about an optimum balance of strength, toughness, and machineability. Mechanical properties in these two conditions would be approx 135,000 psi yield strength, 155,000 psi ultimate tensile strength, an acceptable low temperature toughness of 15 ft/lbs at -100 deg F, and a Rockwell hardness of C- 31 to C- 33.
The "A" condition (solution annealed with no subsequent heat treatment) would be a possible choice for barrel steel. Yield strength of 110,000 psi, ultimate tensile of 150,000 psi, but impact properties listed only at room temperature (30 ft/lbs). You could interpolate impact toughness at lower temperature, but that's unacceptable for gun work. Only tests at the lower temperatures would prove its actual toughness. I'm sure they've been done, but I couldn't find them.
I mentioned the difficulty of correlating mechanical properties. This steel is precipitation hardened, and the soak temperatures (not soak times), have a drastic effect on its mechanical properties. The H-900/925 heat treat gives ultimate tensiles approaching 200,000 psi, but simultaneously improves toughness somewhat. By contrast, the H-1150 treatment tempers the hardness back to about 28 Rc, lowering yield strength back to 110,000 psi, and ultimate tensile strength to about 145,000 psi, but greatly improves low temperature notch toughness (to approx 45 ft/lbs at -100 deg F).
Sirrocco mentioned corrosion resistance as an advantage. My take on the issue is probably significant improvement in erosion resistance over 416 R. Increased barrel life. It's the primary reason I bought a LW Blackstar barrel off this site quite awhile back and chambered it for .30 x .378 Wby. I found the barrel to be tough (crunchy) and had to do some experimenting to get a nice chamber finish. The tenon was not difficult with carbide tools. I haven't been able to shoot the rifle enough to reach any conclusions on accuracy, let alone barrel life. Bottom line, I still don't know how accurate it will be or how long it will last. My opinion however is that a 17-4 PH barrel can be as good as a 416 R barrel, and will last longer.
I've been wanting to research this steel for a long time. Gary had pretty well covered it except for the low temp toughness, but I tried to sum it up so that even I could understand it.
Tom