It may be because that M06 is considered more middle or long distance interaction than B3LYP. 

Hello,

This article can be helpful. It compares the performance of 24 different density functional methods for calculation of binding energies and relative energies.

The Performance of Density Functionals for Sulfate–Water Clusters, J. Chem. Theory Comput., 2013, 9 (3), pp 1368–1380.

http://pubs.acs.org.ezproxy.its.uu.se/doi/abs/10.1021/ct4000235

In addition to Radia Ayub's suggestion above (for which the correct link is http://pubs.acs.org/doi/abs/10.1021/act4000235 [remove the ezproxy part]), as that paper is a bit too optimistic for M11 I would also recommend a paper by the same authors that critically examines the Minnesota functionals, titled "How accurate are the Minnesota density functionals for non-covalent interactions, isomerization energies, thermochemistry, and barrier heights involving molecules composed of main-group elements?" ( http://pubs.acs.org/doi/abs/10.102a1/acs.jctc.6b00637 ).

Sir Mustafa Karakaya

Here is some reference for the different functional DFT, DFT-D and functional hybrid DFT-D for good parameter prediction and interatomic distance and HSE for gap energy