The first warmonger looks like a huge jerk. Everyone hates him. He has to deal with this giant, sprawling, unhappy empire and no one will trade luxuries or make research agreements.
The second warmonger starts a fight with everyone's enemy, so he has friends, or at least not-enemies-at-the-time. If he finds a useless city he doesn't need to burn it and suffer the unhappiness. He can instead liberate it. That instantly saves all the happiness and pushes the enemy army out, so it isn't going to be retaken. Even better, it makes a friend for life and makes you look like a generally great guy. Want your ideology to pass? They've got your back. For diplomatic victories they're worth more than a handful of city states and aren't going to get flipped by coups.
Even if you're going for conquest it works out just fine. You aren't the jerk who captured their original capitol. You just happen to have it. You can dump other cities on them too. There isn't too much risk of strengthening a potential enemy, since they're likely to be technologically and socially backward due to not existing for a while, and they weren't strong enough in the first place. The cities are missing buildings anyway.
Of course you don't want to be too late to the party, or else you're going to be trying to push the snowball back uphill.
The second warmonger starts a fight with everyone's enemy, so he has friends, or at least not-enemies-at-the-time. If he finds a useless city he doesn't need to burn it and suffer the unhappiness. He can instead liberate it. That instantly saves all the happiness and pushes the enemy army out, so it isn't going to be retaken. Even better, it makes a friend for life and makes you look like a generally great guy. Want your ideology to pass? They've got your back. For diplomatic victories they're worth more than a handful of city states and aren't going to get flipped by coups.
Even if you're going for conquest it works out just fine. You aren't the jerk who captured their original capitol. You just happen to have it. You can dump other cities on them too. There isn't too much risk of strengthening a potential enemy, since they're likely to be technologically and socially backward due to not existing for a while, and they weren't strong enough in the first place. The cities are missing buildings anyway.
Of course you don't want to be too late to the party, or else you're going to be trying to push the snowball back uphill.