Sorry, but there's a massive improvement in load times for Half-Life on the PS2 release compared to the Dreamcast build, both in terms of length of save time and how numerous the saves are. The saving also isn't screwed up like on the Dreamcast when sometimes the VMU won't even be large enough for a save. The saving is much more efficient space wise with the PS2 release and was never refined on the Dreamcast build everyone has.
The PS2 version also supports any USB mouse and keyboard and not just Dreamcast accessories. The dual analog stick is far better for the game then the single analog stick of the DC controller. The textures have also been refined further and the character models have a higher polygon count over the Dreamcast version. And the frame rate is smoother and more consistent on the PS2 release. The Dreamcast build going around was supposedly never optimized, which leads to a fairly low fps and more inconsistency due to not being the final build. And Decay is actually an exclusive, unlike Blue Shift that has been ported elsewhere (PC).
Still, it's worth the download and cd-r.