Wouldn't you actually be paying more taxes as a one person company? Why does it matter if the company has only one client and one employee if everything is paid properly?
Because as managing director you don’t have to pay pension insurance (and others). So if you are employed, the social system will get more contributions.
You have to pay into it of you're employed and make below ~4800€ (before taxes) a month.
It's rather much % of your income, so you can save rather much by not paying it.