Why is DMSO more polar than other solvents, yet it dissolves ionic compounds worse? I'm working right now in the solvent importance in ionic character, and I noticed how a binary salt ($\ce{CuCl2}$) dissolved better in methanol than in dimethylsulfoxide, and in contrast, a coordination compound (Cu[salen]) dissolved better in DMSO that in the aforementioned solvent.

It doesn't make a lot of sense to me considering these properties I found:

DMSO:


Dipole moment: 3.96
Dielectric constant: 47


Methanol:


Dipole moment: 1.71
Dielectric constant: 33


I would have expected the binary salt to dissolve better in DMSO rather than Methanol, and the inverse in the coordination compound yet it didn't happen like that. Is there a intermolecular detail I'm not considering? An hydrophobic-hydrophilic portion in the structure? Thanks everyone.
Having large dipole moments and dielectric constants, as DMSO does, does not imply that it has the ability to solvate ionic compounds like $\ce{CuCl2}$.  

Although both methanol and DMSO have oxygen atoms with their lone pair of electrons to help solvate cations, there is no corresponding functionality in DMSO to solvate a small, inorganic anion like chloride.  Methanol on the other hand can solvate chloride via hydrogen bonding in the same way that water does.  

These properties are not necessarily applicable to a coordination compound, so there is no reason to expect methanol to act as a better solvent than DMSO in this case.