The US equivalent of the CAP is the farm bill. The estate tax in the US tends to benefit US farmers more than similar taxation in Europe.
Then: a number of sticky points will resolve around intellectual property rights such as ACTA:
“In 2012 the newly-appointed ACTA rapporteur, British MEP David Martin, recommended against the treaty, stating: “The intended benefits of this international agreement are far outweighed by the potential threats to civil liberties”. On 4 July 2012, the European Parliament rejected the agreement in plenary session, with 478 voting against the treaty, 39 in favour and 165 MEPs abstaining.”
It is certain even watered down versions of such agreements will be blocked by the more liberal minded parliaments such as the Swedish one. Both the EU end US tend to negotiate these agreements with too little prior debate and an unformed public opinion. Then when the initatives reach national parliaments, public opinion and parliamentary majorities form against them.The treaties tend to overwhelmingly favour the interests of intellectual property owners because the latter are far better organized than the rather ad-hoc coalitions that form in response.
Of course the same can be said for agriculture: the agricultural lobbies heavily influence the drafting process.