The ideal solution would be for both to push OpenGL as hard as they can.
I agree, but I can't see things clearing up until later this year when AMD say the API will be open to scrutiny by all.
Mantle only exists because of AMD's console hardware. They saw an opportunity to use that position to their advantage in the PC space. There are only so many developers, so much time and so many titles in development at any one time. If AMD can make cross-platform development more straight-forward for devs, while also promising greater performance than DX on like hardware, that's potentially a huge plus for their Radeon line.
But, AMD need adoption for Mantle to be worthwhile and I don't think they'll see that adoption unless nVidia write a Mantle driver for Geforce GPUs. Without that, devs will have to write for two renderers if they want to sell enough copies to make money on PC. Writing a game for multiple renderers for dubious benefit is not going to be popular with many.
Studios are all ready tooled up for DirectX development and some popular engines already have OpenGL renderers. It's going to be a tough sell for AMD.