I have both lenses.
I would lean towards the 70-300mm. It is a pretty amazing lens. The IS is truly astounding and the sharpness is pretty amazing, especially at 300mm and wide-open. I haven't really noticed a sharpness difference between either one. They seem about the same.
If you don't think you would use a 1.4x and would be more inclined to want a compact "all around" lens to go everywhere, the 70-300 is the way to go, IMO. The 300mm gives you the option of 420 with the 1.4x, but my copy seems to have a lot of distortion with a 1.4x, so I don't even use it all that much with the 1.4x. The IS is not the latest generation, and while it is not bad, it is pretty clearly out-classed by the 70-300.