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A 180 grain Sierra GameKing loses a lot of penetration above 2800 fps, and fails to open below 2100 fps. If your load will give you 2800 fps at the muzzle, then your working range is 0 to 400 yards, where the bullet drops below 2100 fps.
A Partition is a much tougher bullet. It hangs together well at 3100 fps, and reliably opens at 1800. That gives you a 0 to 500 yard working range with your 06, or a 0-650 yard working range with a 300 Mag.
Penetration is actually fairly constant over the working range of most bullets. Partitions give an extra 2-3" of penetration, which is worthwhile. The Barnes X gives even more, and I suppose the same is true of their other offerings.
I'm no expert on bear hunting, but my thought would be either 200 or 220 grain Partitions for them, and maybe 180 grain Partitions for elk or meese, and standard 165 grain bullets at maybe 2850 fps for anything smaller.
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