But you're looking at prices, rather than yields? It's not really going to work in any intuitive fashion this way... Can you see the schatz yield somehow?
The current yield of the 4th/5th Euribor contract is 2.002 whereas for the Schatz Dec09 it is approx 1.785. Do you think looking at the absolute difference between the two yield could help decide anything about the direction of the duration neutral trade?
Well, ideally, you would need to calculate the EURIBOR leg yield as a weighted average of a number of ER contracts (7 at the moment). However, the 4th and/or 5th contract should serve OK as a proxy. You should take the spread, which will give you the EUR version of the 2y TED spread.
Generally, in the world of rates, these types of trades involve buying/selling a bond (or repo or derivative, such as a future) vs selling/buying a DV01-weighted amount of an IBOR derivative. A position structured properly this way (both outright and bucketed DV01s exactly offset) doesn't expose you to any outright rate risk or curve risk