Let's look at Doublade.
Thanks to its sky-high Defense stat backed up by an Eviolite and an excellent defensive typing, Doublade is a great check to strong physical threats such as Cobalion, Terrakion, and Lycanroc-D, although it must be careful, as the latter two commonly carry coverage moves to hit it super effectively on on the switch. It also sets itself apart from other walls for its great Attack stat, ability to sweep late-game, and access to Swords Dance and Shadow Sneak. However, due to Doublade's overreliance on Eviolite, it struggles to safely switch into foes it's supposed to like Mienshao and Heracross, as they commonly carry Knock Off. Furthermore, due to its low Special Defense, Doublade should not stay in on special attackers that aren't weak to Shadow Sneak such as Kingdra and Keldeo.
Thus, while its Def and Atk are great, its Sp.Def is bad, only at 49. Plus, it heavily relies on Eviolite for its extra bulk, which is good to note since many Pokemon carry Knock Off. And its tier is UU.
(Unfortunately there is no explanation for Aegislash in OU, I guess I have to write in my words.)
Unlike Doublade, Aegislash can rely on another items since it is fully evolved. Even if you don't run a King's Shield and go for coverage moves and Swords Dance, its staying in Shield Forme at starting makes it really dangerous since he has Solid Defense on Shield forme. Swords Dance boosts his awesome attack to sky high levels, staying in Shield forme. If you require speed, then it also learns autotomise. He can act a setup sweeper with having Weakness Policy and Swords Dance staying on his Shield Forme and gets Shadow Sneak for dealing with faster foes.
Overall, Aegislash is better than Doublade, as knock off is common in the meta plus Weakness Policy Aegislash is much better altogether than Eviolite Doublade.
Hope this helps!