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The short answer is that it depends. While the exact velocity would vary with the load you use, you can expect to get 2450-2550fps out of a 150gr bullet out of that barrel length. This would give you a slightly higher velocity than the .30-30. However, with the .308 Winchester your bullets will usually have a much higher ballistic coefficient (~.400) than those fired from a .30-30 (~.220). This, combined with their slightly higher velocity, will result in a generic 150gr .308 bullet shooting slightly flatter and hitting a little harder than a generic 150gr .30-30 bullet.
Using a these rough figures in a ballistic computer shows that the .308 bullet will have over 1000 FPE all the way out to 400 yards. With a 250 yard zero, the bullet will hit 4.59" high at 150 yards and 5.39" low at 300 yards, which is adequate, but not great for hunting purposes. For comparison, a generic .30-30 load would drop below 1000 FPE between 150-200 yards and be over 15" low at 300 yards with a 200 yard zero.
Bottom line: the .308 will work better than a .30-30 out past 200 yards and still hit plenty hard enough to get the job done even when fired out of a 16" barrel.
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