Do I even need a SIM card for Switzerland if I live in the EU?
If you live in the EU, calls and internet usage on your cell phone are the same whether you're at home or elsewhere in the EU. Switzerland is no member state of the EU though. Some providers do count Switzerland as a EU country. Some don't, so you'll pay more.
Try to estimate how much you will call and how much data you will need during your stay. Check the rates of your provider for calls and data in Switzerland. It can still be cheaper to buy a SIM card. For fast internet, and especially if you travel with multiple people, renting a mobile Swiss Wifi hotspot is an excellent option.