[Barbu]

I think that the para has a smaller dipole moment due to the greater symmetry, but maybe the ortho interacts poorly with the stationary phase because it is more bulky, so I don't know.

[opsomath]

In my opinion, the ortho compound will stick harder to silica (assuming you mean a normal-phase TLC experiment) because of the positioning of the two groups on the same side, meaning that both groups can hydrogen bond to the surface at the same time.

The overall dipole moment of the molecule is actually not very important.

I will say that these two molecules would be extremely, extremely difficult to separate by most forms of chromatography.

[Babcock_Hall]

I would think about which molecule has the greater dipole moment.

[Enthalpy]

Their melting points should differ significantly, suggesting an alternative to TLC.

In TLC, could the solid be taylor-made? If the solid has fewer active centers whose spacing matches the ortho- compound, it will interact with the ortho- more strongly than with the para-. Say, if the solid is a polymer, bearing as side chains these same ortho- groups on phenyls, possibly as alcohols to be more sticky. Then, of course, said polymer should better not dissolve in the liquid...