When puppet, chef or ansible are simpler solutions than package manager?

I'm new to above deployment and configuration tools. I have typical need to install and upgrade on a target machine a customized and configured webserver, maybe reverse proxy, database, required runtime for interpreted languages and such. My distribution already has a package manager that works. I can create and distribute my own packages containing preconfigured software and install/upgrade them over ssh. Where should I expect this solution to be insufficient and opt for mentioned tools?