Rifled bullets do not tumble -- they yaw
at least modern boattail designs.
If impact velocities are high enough (variable depending on bullet materials, jacket type and thickness) depending on the tissue type and depth - then the bullet will do something else -- in the case of C77/SS109 type ammunition, it often fragments at the cannelure.
You can open a whole different can of worms on ammunition types - but if we stick to a standard NATO ball round, you will see reliable fragmentation above 2500fps impact speed (once again everything else being equal), and enough depth of tissue (lets say 6-7" for this purpose).
Below that the bullet will yaw but will stay together barring an impact with bone (which will also cause secondary fragments).
People generally die of bullet wounds one of two ways 1) CNS hit with destroys the brain stem 2) Lack of Oxygen to the brain. With #1 your looking at a very small target area - generally not viable for the general purpose forces regardless of range.
With number #2 - your looking to may the target leak blood like a faucet - either internally or externally by massive damage to organs and the circulatory system. (which is why Center of Mass shooting in a misnomer, its should be high thoracic area, or center of visible mass for a reduced signature target.
Given the C77/M855/SS109 bullet design and fragmentation envelope - it really does not matter if you shoot the target at 250m with a C7 or C8.