The US talks about Open Skies on transatlantic routes. Europe talks about an Open Aviation Area encompassing the EU, The US, and the routes between the two.
That is the gulf between the two positions.
The US talks about market access, and pricing freedom. In other words, any US or EU airline, flying any EU-US citypair, charging what it likes.
The EU talks about this plus – US access to EU domestic, EU access to US domestic. In practical terms, these freedoms are no particularly big deal. Much more important is a process of a harmonisation of the competition rules – the two sides have very different interpretations of what constitutes anticompetitive behaviour, abuse of dominant position etc, also there are different rules on what constitutes State Aids, bankruptcy protection etc. Then there are big issues on divergence of security rules, for example.
Ownership & control is a big sticking point, not (only) because of US protectionism, but because the starting point in the harmonisation process is different on either side of the Atlantic. A US airline has to be 75% US-owned, whereas an EU airline has only to be 51% EU-owned. This means that, in a process which eventually abolished majority-ownership rules, the US would have to move unilaterally to the EU level before the two could contemplate moving in step to something less restrictive.
In the world of aviation bilaterals, where every demand from one side is subject to a quid pro quo on the other, giving ground unilaterally is something big strong countries don’t do easily.