I was wondering, does the older card (HD 6870) have better specs than the newer card (HD 7770)? (In particular, I'm looking at the shader processors.) The older card is discontinued... does it mean that there were problems with it and I'm reading the specs incorrectly?
True one is newer but its from a lower tier family.
With AMD cards the first number is the generation so you are looking at a 6 series card vs a 7 series card.
The next number is the family within the generation. This has been pretty solid for a good few years now so you are looking at a higher positioned family of older cards compared to a lower positioned family of newer cards.
Performance wise the 6870 is about 20-25% faster. In some games it would make the difference between playable and not really playable at 1920 x 1080 resolution.