Yes and no. Student status does not lead to reduced taxation in Germany (that should hold for non-locals, too). Instead, low incomes and scholarships are not subject to tax, which is probably what you are referring to. The maximum amount for scholarships before they are subject to taxation is said to be higher for non-Germans, though. As a student, health insurance is also cheaper.
You are unlikely to get the cheaper health insurance as a PhD student as well. Depending on the state in which you do your PhD, you may or may not be allowed to enroll as a PhD student, so you may lose benefits such as cheaper food in the student canteen. Other than that, see the links provided in the comments to your question by Wolfgang Kuehne, as the taxation situation is very much dependent on how your PhD studies are funded.
However, being subject to taxation and full-fee health insurance is not necessarily bad, as if you manage to find a 100% paid scientific employee position (which is not uncommon for CS), you will see that the net income is actually quite ok - even if you take the higher accommodation cost in Munich into account.