Is there any reason to use an international exchange instead of a local one?

I'm currently using a local exchange to buy BTC (I'm from Europe).

Since the exchange is under regulation by the local financial authorities, it is pretty obvious that the state would have a very easy time investigating my activity.

Not that I'm doing anything (currently) illegal, but this just doesn't sit right with me. Is there any reason to use an international exchange instead? Are there any exchanges, for example, that are more restrictive in handing out customer information to foreign states?