DVI (and, for that matter, any digital signal) should offer you a somewhat clearer picture... Though to be honest the change in standards was made to address other issues unrelated to picture quality.
Digital signals can drive higher resolution screens at faster screen refresh rates.
The quality difference between a VGA signal and a DVI-D signal pushing a resolution of 1920x1080@60Hz is going to be negligible (Under 99% of circumstances. You could be in a fringe case where there is a ton of EMI near the video cable in which case DVI-D would provide better picture when it worked at all.), if there is one at all.
That being said, there
doesn't appear to be any circuitry for converting between DVI and DP so there won't be any difference between the signals does seem to be some circuitry to convert the signal so it could impact video quality though it is highly unlikely to have a major impact. Aside from things like loose connectors in super cheap products, you should be fine getting any inexpensive adapter (Just stay away from the $0.14 adapters from china).