Alexander vs. Barbarossa

Outside Conquest, Barbarossa's utility outweighs Alexander's higher stats even with the latter as a gold gen.

Barbarossa has aura and Leadership which reduces the atk of the enemies he attacks or successfully counters. This slightly reduces the dmg received by him and nearby allies. His aura boosts the fighting capability of nearby inf units or gens, ie. one of the most commonly spammed units in the game.
The Petain-Barbarossa combo enabled a successful strategy of fighting a war of attrition in many Legends battles, only outshone by the aggressive blitzkrieg strategy enabled by cav gens.

As for Alexander, his raw status is superior to Barbarossa's, but he has an atk primary skill and Spy. If the enemy attacks another ally instead, Alexander would have automatically failed as a meatshield.
Spy does reduce the def of enemy units, but boosting your allies' atk power arguably leads to the same output and outcome.
Moreover, cracking cities should be left up to Archers and Arty units, not inf or cav units. His fort cracking abilities mainly shine on certain Conquest maps and Campaigns in which a gate located in a narrow corridor has to be assaulted while melee units suffer from Archer attacks launched from behind the walls.