Finally, if the desired amount of pixelation lines up, certain lower-resolutions scale up perfectly to both 720p and 1080p -- for example, if designed for a logical resolution of 640x360, then it scales perfectly by a factor of two to 720p and by a factor of three to 1080p. If that's a good match for the desired amount of pixelation, this is definately the way to go because it gives pixel-perfect results in both cases, with no additional work, without starting from over-size sprites, and the scaling can be done in-engine. 640x360 is probably the only practical resolution if you want to use every pixel on the screen in both modes (320x180 is the next one down, and that's really pixelated already). Others are decent candidates if you can accept some letterboxing (say, 420x240 -- although that's not perfectly 16:9 either).
I agree with this third point. Aim for a fixed widescreen resolution, up\down scale to the display settings later, in real time.
Make a style-guide with your team where you choose the best fixed resolution that gives you enough detail for pretty graphics while still following with your capacity to generate content for that resolution (that is, your art and animation budget), and finally what general visual style you want your game to have.