We started at 1920x1200 with everything set to "Gamer" on the Sapphire Radeon HD 4850 X2 and our fingers crossed, and the Sapphire fell flat. We lowered it to 1680x1050, and it was still not happening. So then we had to lower some in-game settings. We started with lowering some of the less conspicuous settings like Volumetric Effects, Post-processing, Game Effects, and Particles, but it wasn't enough. We then lowered the Shadows Quality option and that helped a lot, but it was still choppy and unpleasant. Ultimately we had to choose between lowering the Shader Quality or the Texture Quality setting. Our observation was that the Shader Quality setting had a much more dramatic impact on image quality, so we opted to set the Texture Quality option to "Mainstream" to make Crysis: Warhead playable.
Meanwhile, both the Radeon HD 4870 1GB and the NVIDIA GeForce GTX 260 were able to play Crysis: Warhead at 1920x1200 with 16X AF and all in-game settings at "Gamer", but without any level of AA. Between these two video cards, the Radeon HD 4870 1GB gave us slightly better performance, but certainly not enough to declare it a clear winner.