I used semiemperical calculations (PM3) to find the local minima of the conformations shown in the image attached. Experimental results (though the article was from 1979), concluded that 1,2-dimethoxy benzene had antiplanar conformation, and the mehoxy substituents pointed in opposite directions. The conformer search with Molcular mechanics ave the same results.

But when my friend used DFT calculations (with a really good basis set, B3LYP/extended SV Dunning-hay), the planar conformation showed up to be the stable one.

Seen from a chemical point of view, with all our paradigms, I cant see why the planar conformation would be the correct one. With the planar conformation, there must be som kind of conjugation with the aromatic ring, in both of the substituents. This doesnt make sense, since there would be a large negative charge on each carbon next to oxygen. (methoxy group is ortho-para directing).

Does anyone shear my pont of view, or should I thrust the DFT calculations?

I don't think I'm understanding the conflict here.  Your posted image shows the antiplanar conformation to have the lowest energy.

Thats right. But you see, this is semi-empirical calculations. I can't trust them to be accurate for my use. And when more advanced ab initio calculations shows the opposite, and the experimental results (that article from 1979) support the MM conformer search, I really get condused!

My intuition says the antiplanar conformer is the right one.