This is when ATI/AMD did a bit of "slight of hand"/confusing name change (for marketing). In terms of gigaflops the 5850 is about 40% more powerful (2088 vs. 1488), than a 6850. Flops aren't everything, but that's a considerable difference(40%). Even Tom's GPU Hierarchy Chart ranks the 5850 one tier higher (that refects real world frame rates). And both are DirectX 11 cards and built on the 40nm fab process.
By today's naming the 5850 would have been called the 5950. A number that wasn't used back then. And 5970 was the dual GPU card, not 5990.
Some cards were a direct "carry over".
Example: the 5770 > 6770 (you can also crossfire them).
A 5850 likely would be several months older thou (depending on production date). As it was released in late 2009, over a year before the 6850. Anyway, the 6950 was the sucessor to 5850. Since it was built on the same fabrication process, AMD had to use a "sledgehammer" approach to make it graphically more powerful... it uses more electricty (200 watts vs. 151).