My experience tells me to first select the bullet, then the powder. And my 308 barrel does not like the 178. It likes the 175 SMK as well as the 185 Berger Hybrid. The 155 scenar not so much, nor the 185 Berger Juggernaut. If you find the right bullet, the powder will make less of a difference in accuracy, especially at short range. For long range, different powders have different fill levels at different velocities / pressures. I have found that if I max out my fill level to where I am running a slightly compressed charge, I get lower SD's. That is where powder measures. You can also squeeze a little extra velocity out at roughly the same pressure with some powders.
But ultimately, it is bullet first. I have gotten to the point that before I even bother to do load development, I will load a bullet up at safe pressures with whatever powder, seat it close to the lands, and just see if it shoots. If it does, then I go back and mess around with charge weights and where to seat it. Otherwise I don't bother. You can waste a lot of time tweaking to get an MOA bullet to shoot .75 MOA in you barrel, but if you start at MOA, you are probably not going to get to under half just by tinkering. And that is my goal.