To fly "equally well" you'd need the plane to basically be symmetric front-to-back. Which would involve some pretty horrible wing geometry (identical trailing and leading edge shapes, no washout, etc.) You'd also probably have to forgoe conventional controls, as it's hard to see how you'd get decent flaps, ailerons, spoilers etc to work, unless you simply doubled up on each (completely moveable LE and TE).
You'd also have to do something about directional stability and control, maybe having to have fins at each end? It'd be one ugly SoB whatever you did.
Even with active controls to make it flyable both ways, it'd be hard to avoid performance degradations, which I assume is included in "flies equally well"
One thing you could do is abandon the whole wing thing and go with some kind of rotorcraft. You get a degree of automatic symmetry fore/aft from the design that way. Hang a bubble underneath contra-rotating blades and maybe that's not far off the mark?
Interesting question!