u/Mother_Variation_827

• Vader is always displayed by Palpatine as his right hand man because everybody fears him and his own power backs it up. He's a 1-man-army.
• Thrawn is a tactitian who knows how to read people. He is most useful when it comes to hunting down traitors/rebels. He does not choose a "swift victory" but a dissection instead in order to know the summation of the enemies to fully extinguish their flame.
• Despite his tactical advantage over both Tarkin and Vader, it seems he is not being favored so well by Palpatine due to their difference in the views of the Empire. Thrawn is very vocal in disagreements.
• Tarkin who the emperor closely knew since the Clone Wars seems to be the one to manage a high command of armies. He can even bully Krennic. I'm not so surprised if it was Palpatine who instructed him to steal the "glory" from the construction of Death Star. It was probably to prevent the outer circles from gaining too much power.
• Tarkin is a master in using FEAR through power which Palpatine is much in love with. Considering that they control much of the galaxy now, Tarkin is the right man to entrust the Death Star with. He's the guy you use for a "One-fell swoop" attack.
• Other than this, Palpatine sees that he holds all the power, so it clouds his judgement and believes his power will never tumble. Thus, Thrawn is not much needed as Tarkin and Vader are (since they are the ones to be used primarily for creating fear) during EP4.

But to sum this one up, Palpatine keeps all 3 to his advantage while making them believe that they probably have a chance to replace him one day..

This is how I understand it. I might be wrong. Feel free to correct me.