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...isn't drag relatively negligible...
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Air resistance is pretty significant. It's often neglected in problems given to students--not because it's negligible but because it can be quite difficult to calculate.
The more aerodynamic object will accelerate faster (since there's less force from air resistance fighting that acceleration) and will eventually reach a higher velocity before the air resistance balances the force of gravity.
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I'm not sure if the bullet gets there, starting from the ground and all.
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A bullet will travel upwards thousands of yards--experiments have shown a 30-06 rifle bullet will reach a height of around 9000 yards. That's enough time for the bullet to attain terminal velocity on the way down.
Interestingly enough, the person (Julian Hatcher) who did the experiment calculated that the bullet would have attained a height of over 21 MILES had there been no air resistance. Drag can not be neglected.