Not so simple
The concern in the data-protection part is not about snooping by government but by corporations, since US privacy rules are nearly non-existent compared to Europe.
For the SWIFT financial data, the EU governments actually want it, as the US has data-mining capabilities the EU lacks. The tension is between the EU executive (the European Council, representing the heads of EU governments) and the European Parliament.
The fact Catherine Ashton was on the receiving end of surveillance as a human-rights campaigner should mean she is sympathetic to the MEPs' view, but she is constrained by her position and her need to work with EU member governments to get anything done.