In Task-Oriented Dialogue (TOD) systems, correctly updating the system's understanding of the user's needs (a.k.a dialogue state tracking) is key to a smooth interaction. Traditionally, TOD systems perform this update in three steps: transcription of the user's utterance, semantic extraction of the key concepts, and contextualization with the previously identified concepts. Such cascade approaches suffer from cascading errors and separate optimization. End-to-End approaches have been proved helpful up to the semantic extraction step. This paper goes one step further paving the path towards completely neural spoken dialogue state tracking by comparing three approaches: (1) a state of the art cascade approach, (2) a locally E2E approach with rule-based contextualization and (3) a completely neural approach.