Fundamentally, there would have to be a continuation of the Catholic doctrine that communion with the Roman bishop is necessary for full communion with the church, as he is its chief pastor and successor to the Apostle Peter.
How this primacy is exercised can be tweaked, of course, but what must be maintained is what Cyprian of Carthage said back in the 3rd century, that there is one chair of Peter centered at Rome, from which the church’s unity proceeds. And we must be in agreement with Irenaeus of Lyons from the 2nd century, that all churches must look to and be in agreement with church of Rome and its bishop.
Otherwise, from the Catholic perspective, most of the theology is fundamentally the same. My personal experience is that Orthodox tend to think Catholics are way off the mark, even in differences of theological or sacramental approach, while Catholic thinkers tend to be more receptive of a diversity of thought with regard to how liturgy and theology can be done. Just my experience.
After all, look at those Eastern churches that have come into full communion with the Catholic Church. Under the best circumstances, they have kept their liturgical, legal, and theological traditions – even equivalent to their Orthodox counterparts – all the while accepting the primacy and supremacy of the bishop of Rome, as successor the the Apostle Peter.