Crossman has had .177, .22, and .25 prechargeds around for a while and this looks like a big brother to those. The biggest advantage I can see is how quiet they are, since the new one will be subsonic. And you can load them up on air to fire a couple of magazines, likely all you'd need if you were on a day trip hunting. You can knock a steel silhouette over at 75 yards, so it has some punch. You can see a video here.
There are bigger airguns around. The Sam Yang Big Bore 909 in .45, 190 gr., will punch a hole through a concrete block, and runs about six hundred bucks. It's a single-shot, and you can get eight or so at full power, then velocity drops off.
Of course, power drops off in all PCP weapons as the reservoirs empty, so point-of-impact must be adjusted with the sights or scope.
Since the .357 still seems to be a prototype, there's a lot unspecified, but it seems that it will shoot most commercial bullets in the caliber, and hollow-base lightweights will zip out faster.
As far as I can tell, these rifles (and a pistol) all produce subsonic velocities. This isn't a major handicap for a quiet weapon, and a lot of things have been knocked over and killed with low-velocity rounds. Your basic .45 ACP hardball runs 800-900 ft/sec. But you probably won't be hunting bears with these. Well, at least not after you find the first one ...
On the other hand, you need a scuba tank or a special compressor to fill them, though in theory you could use a hand pump if you are on steroids and have all day.
My experience with airguns is that the seals eventually go out. 2000-3000 psi is a lot of pressure, especially if are in the field and if you drop the sucker. A hundred-year-old rifle kept oiled in a closet will still shoot just fine. I suspect the life of an airgun is considerably shorter.
The cost puts them in the high range for comparable gunpowder weapons -- $500 for the little ones, and $1500 projected for the .357, so it's not a casual buy.
It would make a good urban hunting rifle for small game, and certainly an 800 ft/sec round would give a burglar pause. As I understand it though, you aren't supposed to leave them charged for long periods, and asking a housebreaker to hold on while you pump up your air rifle might be something of a drawback ...