Its unseemly to directly get involved in US politics by targeting specific congressional districts to send a message. That's the sort of stuff many Americans were outraged about after the 2016 election.

To be honest I am not sure. From what I have read you were right on the first guess. When China applies tariffs it is a single political body making the decisions, while the EU needs to deal with a lot of different national interest groups all applying to get the benefits of tariffs for their product or service. Back when Trump started doing his initial rounds of tariffs and inviting reciprocation from China and the EU the Economist had a nice map that showed the regions impacted by the tariffs from the EU vs. China. The EU tariffs were all over the place and a lot of them hit west coast areas that competed with the EU but had little impact on the decision-making, while the Chinese tariffs looked like a 2016 electoral map. (The latter was probably helped by the fact that China imports more cereal grains from the US than does the EU so they had an easy way to hit midwest and great plains states.)