It is most often not the bullet that shoots proportionately better or worse at greater distances,but rather the rifle. For example, the Lee Enfield Mk III was famous for shooting better groups at 1000 yards due to some peculiar barrel/rifle harmonics,
Checking the standard deviations of your loads will tell you a lot about the potential long range performance. A load with a stnadard deviation of 15 fps will give you an extreme spread of velocity of about 45 fps. In contrast you may also have a load that shoots exceptionally accurate groups at 100 yards, but has an SD of 50 fps. A load like that will give an extreme spread of 150 fps and that will show up in greater vertical dispersion at longer ranges, and with any wind at all, will create more horizontal dispersion as well.
Conseqently, if shooting at long range, you will probably be better with a slightly less accurate load that has more consistent velocity than you are with one with a high SD but great short range accuracy. In general loolking at the SD tends to take out most of the surprises when shooting at longer ranges.
Where bullet issues come into play is usually a mismatch of the barrel and rifling. Using the right barrel twist and or the right weight bullet for your barrel twist tends to ensure consitency at longer ranges. The old argument is whether 55 gr shoots well in a 1-7 twist barrel. It depends on how the quality of the bullets, how picky you are in terms of accuracy, how high the velocity happens to be, and how far you are shooting, but in general bullets that are over stabilized tend to yaw and fly what amounts to barrel rolls through the air for a distance before they settle down.
The yaw and precession effects from less than perfect bullets spun at excessive rpms increase dispersion slightly over short ranges but greatly increase dispersion over longer ranges as they don't consistently settle down pointing in identical directions with identical vecotors, so accuracy is much worse than expected at long ranges. Bullets that are understabilized tend to yaw toward the end of their flight paths, so they may also shoot well at short range, but have poor accuracy at long range.