Uber and OU.
Gen 7 (Uber)
A Steel / Ghost typing makes Aegislash an excellent Xerneas and Mega Lucario check, and it cannot get trapped by Mega Gengar, Gothitelle, and Dugtrio.
It can also check other powerful attackers like Deoxys-A, Tapu Lele, and non-Fire Blast Mewtwo.
Aegislash isn't 2HKOed by any of Xerneas's coverage moves due to its good bulk, setting it apart from other Steel-type Xerneas answers.
King's Shield allows Aegislash to punish physical attackers and play mind games with the opponent.
It can punish its switch-ins like Primal Groudon, Yveltal, and Ho-Oh with Toxic.
Aegislash also has decent damage output due to Blade forme's good attacking stats.
However, many powerful and prominent physical attackers overwhelm Aegislash, including Primal Groudon, Marshadow, offensive Necrozma-DM, Arceus-Ground, physical Primal Kyogre, and physical Ultra Necrozma. The prevalence of these threats cuts into Aegislash's viability.
It is also threatened by Dark-types like Yveltal, Arceus-Dark, and Darkrai.
Having no reliable recovery outside of a possible Leftovers means that Aegislash can be worn down over the course of the match. Iron Ball is also the preferred item due to heavily increasing Gyro Ball's damage.
Transforming into Blade forme and attacking at a bad time makes Aegislash open and vulnerable to attacks or setup. This causes it to have to switch or use King's Shield, which forfeits all momentum and gives the advantage to the opponent.
Aegislash can be passive at times and become predictable with repeated use of King's Shield.
Aegislash faces extreme competition from many other Steel-type Xerneas checks like Mega Scizor, Ferrothorn, Celesteela, Necrozma-DM, and Magearna; the former four have better recovery options, and the latter two have more damage output.
Gen 8 (OU)