Well, it works a bit differently as a player than as the GM running a monster.
As a player, maneuvers are more effective at getting the "invoke for effect" because you only get one free tag anyway, whether it's a consequence or a regular aspect. You're spending fate points after that.
As a GM, however, you have essentially unlimited fate points for compels (your only limit being how many fate points you want the player to have at their disposal). Thus, consequences which are going to last for multiple scenes or sessions allow you to continue to exert influence over the player.
The one difference is that consequences make it easier to take an enemy out. Thus, tactically, producing a consequence often has less to do with manipulating your opponent and more to do with "killing" them. As a player. As a GM, they're excellent narrative tools. Forcing players to seek medical help, complicating their lives, etc.