Puppets get 100% manpower, IC, leadership and ressources, while you will only get a small amount plus partisan activity.
So puppets will use the conquered territory more effective than you. In addition, excess ressources will be transferred to the overlord.
In HoI2, it was always a good idea to release Scandinavia as a puppet, since they had good techteams and were able to defend themselves against any medium sized invasion, as well as assisting on Barbarossa. Plus: They built several panzerdivisions and gave them to you as expeditionary forces.
So in general: Puppets lack direct player control, but utilize ressources, IC, manpower, leadership (etc) much better. They do not suffer from Partisans, thus one front less you have to worry about.
So puppets will use the conquered territory more effective than you. In addition, excess ressources will be transferred to the overlord.
In HoI2, it was always a good idea to release Scandinavia as a puppet, since they had good techteams and were able to defend themselves against any medium sized invasion, as well as assisting on Barbarossa. Plus: They built several panzerdivisions and gave them to you as expeditionary forces.
So in general: Puppets lack direct player control, but utilize ressources, IC, manpower, leadership (etc) much better. They do not suffer from Partisans, thus one front less you have to worry about.