You're missing out all the bad parts.
The 5870 was perfect when it launched, excellent price, excellent performance, unless you wanted DX11. Same with the 5850. Only problem was stock. I'm sure AMD gained share with the 5870 versus Nvidia's 2XX as that was the Nvidia cards at the time, AMD were in a league of their own for months. Nvidia cards were better performers when they came out, but their launch was terrible, although as the generation continued the GTX470 probably became the stand out card.
Also, don't forget the driver problems the 5870 had such as the grey screen of death.
The 6970 came out after the GTX580 and was slower, although it had an excellent price point, this is where AMD lost the momentum they'd gained from the 5XXX and 4XXX.
7970 came out as the fastest card at the time, but the price was ridiculous, that was further compounded when the 7950 launched at like ~400 pound. Nvidia then launched the GTX680 at pretty much the same price as the 7950 and out performed 7970 on launch day, and when the GTX670 launched it was much better price/performance and Nvidia were killing it. I remember having a GTX680, for a reference card it was really quiet etc. As the generation went on the 7XXX obviously went on to be better though.
And the 290X had power/temperature/noise as negatives from the bat. Since the 290X AMD haven't exactly been great. The Fury X was hyped up and fell short and went EOL.
Right now 290X performance is all AMD is able to offer right now in bar the Frontier Edition. That's probably causing some issues. How can anyone buy from AMD when they're offering GPU performance from 2013?