It mostly depends on the settings with a less impacting dependence also on the game. Lowering the resolution means that you have a lot more performance to work with and how you use that performance is often what defines which card wins and by how much. For example, if you up the MSAA (which is what I'd do to make up for the lower resolution's increased jaggies compared to higher resolutions), the 7970 GHz Edition wins and often by fairly large margins. If you opt for using different settings such as higher tessellation and others, then the two companies may trade blows more often, but the 7970 GHz Edition is generally the winner right now AFAIK. However, it's also usually not by large margins if there isn't huge MSAA/CSAA.
However, individual games have become greater factors because both AMD and Nvidia have recently updated their drivers and got significant performance gains in some games, but the new drivers from each company favor different games.
I prefer the AMD cards because of their apparent affinity for MSAA and superior overclocking, but that's me.