Elastic Optical Networks (EON), which are able to allocate an appropriate optical spectrum range and modulation format to an optical path according to the client (e.g. IP) traffic demand and path attributes (e.g., physical length or optical impairments), have been proposed to more efficiently utilize network spectrum resources. A control plane is a key enabling technique for dynamic and intelligent end-to-end path provisioning and recovery in such networks. In this paper, we design and deploy two different control planes for EON. One is based on the Generalized Multi-Protocol Label Switching (GMPLS) / Path Computation Element (PCE) architecture and protocols, and the other one is based on a centralized model extending OpenFlow. We detail the protocol extensions involved in the main functional aspects, and we experimentally validate both control plane approaches in a control plane testbed and compare them in terms of path provisioning latency.