There are some certain scenarios where you should prioritize one over the other.
Super early game 00:00 - 07:00
At this point and time you want to prioritize minions over tower hits. The reason for this is because you are super weak and because the towers are super strong, in fact they have a buff on them that lasts the first 7 minutes of the game. I don't know the numbers on the buff but its significant enough that you won't do very much damage at all to the turret. It is much better to focus minions.
07:00 - 14:00 Transition phase
Around this time the first tower falls somewhere on the map. At this time what you want to do is take chip shots at the tower. When you shove the lane attack tower and only attack minions if it gets you a last hit. But make some kind of damage on the tower. If you get the tower low enough you can siege it and eventually take it down. One thing to take into consideration is that the tower gets stronger if there are zero minions nearby. So leave 1-2 minions alive of the enemy's minions and focus solely on the turret. When it gets 3 or more focus the minions.
14:00 - End game
At this point someone somewhere is able to shove the lane super hard and push down the turret. They can then siege the turret if hey can outmuscle whoever they have under that tower or they can roam and force objectives elsewhere on the map. Usually teams are grouped by now so you can actually take a tower with a good tank champion tanking the hits and everyone else pummeling the towers. But you can still repeat the startegy listed in the transition phase, just be aware that you should be strong enough to take towers regardless of whether or not minions are involved.