Two 5970s would be faster when they work right. Even though the 5970 is already 2 yrs old two of them still represent an insane amount of power. If you want to go eyefinity two 5970s would be better, but and boy there are buts.
Many games only support or work well with two GPU crossfire so sometimes it will be like only one 5970 is active. Worst case is that the second 5970 actually has a negative impact on performance which can happen. In those situations two 6970s are faster. Considering you're also either going to use eyefinity or have a single 2560 X 1600 monitor the extra RAM in the 6970s will provide a smoother experience than the 1GB per GPU in the 5970s on more memory intensive games with all the details turned up. Also, because the 6970s are newer they get priority in hotfixes for crossfire support with older cards only being taken care of afterwards. The recent case with skyrim is an example, though I'm pretty sure even a single 5870 can handle it and I haven't bought it simply because I can wait for it to be cheaper
So if you want more raw power and can wait a bit after games come out for proper support and are willing to fiddle with settings to get things to work then go with the 5970s. They may have more issues going forward but when they do work properly you'll be glad you have them. If you want a more problem free solution and can sacrifice the raw power then go with the 6970s. The 6970s will also be better for your electric bill
, but if it was me I'd probably get the 5970s.