I like the change that they made to Tyrion and Jaime's relationship, and I think it will really pay off in S7.

In the books, the two separate under these terms: Jaime tells Tyrion that he was the one who brought Tyrion's wife to Tywin, and lied about her being a whore that he paid to feign love for Tyrion. After the fate that she suffered, Tyrion is absolutely furious. He responds by telling Jaime about all of Cersai's infidelities, mocking his ignorance, and "admitting" that he killed Joffrey. They leave on these terms- and then tyrion kills Tywin. Under these circumstances they both can reasonably despise each other.

However, the split in the show is a lot sadder, and sets up a pivotal moment as the show heads towards the finale. We see Jaime stand up for Tyrion repeatedly-to the Starks, to Cersai, and to Tywin. He even offers to move to Casterly Rock in exchange for Tyrion's life, despite the fact that doing so means a life away from Cersai and his children. When this fails, he frees Tyrion and share a quiet but truly sad goodbye- but as in the books, Tyrion kills their father and disappears. Now instead of hating Tyrion for killing Tywin and for thinking he killed Joffrey and for spewing the insults of Cersai'a infidelity that he constantly hears repeating in his head, he'll be faced with either fully recognizing the evil in his family and forgivinf the brother that he (and the audience) loves and fighting for him one last time, or really turning on him out of love for his father (a complicated relationship) and possibly Cersai/Joffrey/Marcella as well.