If you mean equal parts forward and backwards wound, like an Ayerton-Perry construction, that isn't an inductor, it's a resistor with a circular cross section. It has no interesting properties beyond a chunk of metal the same overall geometry.
If you keep the wires separate, and look at the impedance between them, you have, not an inductor, but (drumroll) -- a transmission line! As a TL, normally you'd not have the wires moving away and towards each other, but paired together, say as a bifilar winding.
What's the difference, then? At medium frequencies, the TL impedance is the average from the geometry (wires far apart have higher impedance; closer, lower), while at high frequencies the periodic change in impedance gives a bandstop filter effect. Meanwhile, the TL being wound up in a helix puts a lot of turns near each other, which changes the velocity and dispersion characteristics.
All TLs have the characteristic that, at low frequencies, they have equivalent capacitance in parallel between wires, and inductance in series along them. Indeed, anything with physical dimensions does, so keep in mind that any real "resistor" contains some inductance and capacitance as well!
Tim