Differences might be noticeable if you can flash the 6970 BIOS onto it, don't know the details about that process though. IMO they're too close in performance. If your games are lagging with the 6870 then they won't be much better with the upgrade.
Way too close to notice I think. Here are those cards side by side in various benchmarks. http://www.anandtech.com/bench/Product/510?vs=540 The extra frame buffer (ram) might help a bit however.