Julian,
If you want to use 802.1X with EAP-TLS protocol then we need both client and server certificate and for EAP-PEAP/TTLS we need server certificate.
In EAP-TLS protocol, client need to trust server certificate and server need to trust client for authentication to success where as in EAP-PEAP protocol, we need password and server certificate for client to authenticate.
Regards,
Pavan