According to several references I found, DVDs are considered the canon, so (sadly from my POV), Greedo shot first.
The Holocron is divided into 5 levels (in order of precedence): G-canon, T-canon, C-canon, S-canon, and N-canon.
- G-canon is absolute canon; the movies (their most recent release), ...
Please note that, as the question noted, the latest release (as of 3/2011, it's "2006 DVD", but the answer might change once the rumored Blu-Ray Star Wars is released) had two versions — the 2004 changed "Greedo short first by a small margin" and the original theatrical "Han short first" version.
Despite both version co-existing on the DVD, the release explicitly notes that the original theatrical version with Han shooting first is "bonus material", and thus not the "main" version. Therefore, Greedo shot first according to G-canon rules above.