Bullet weight in itself is not necessarily a measure of effectiveness on large game. I would certainly expect the 250 or even 200 grain Shockwave to out penetrate a 348 grain Powerbelt lead HP.Many modern bullets, like the Barnes X, are constructed to provide a lot of penetration even in the lighter weights.

Roskoe,you are right weight is not a measure of anything except recoil.
I find a lot of heavy bullets [powerbelts are a good example] to be good varmit bullets but the rainbow trajectory makes it very chancy to shoot any kind of distance with them. On the other hand a properly constructed bullet at the right velocity will shoot flat and penatrate deep. Note the moose and elk that have been taken with 50/40 - 200gr Shock Waves.
I would go to 300gr Shock Waves for Griz or Polar bear though. Lee

The 290 gr in Barnes TMZs is actually a little faster at long range (because of a higher BC) than there 250 gr--- 290 at 200 yds is1458 fpsand the 250 gr at 200 yds is 1435 fps. The energy is greater yet, 1143 ft/lbsfor the 250 and 1368 ft/lbs for the 290. If the heaver recoil from the heavier bullet doesn't bother you, and they both shoot with the same accuracy, the 290 is superior. For deer you may not need the extra energy down range but it can't hurt. Buy the way these are Barnes balistics, not my own personal readings. The 250s seem to shoot slightly more accurately in my Omega, but only slightly.