If you pick up either of those versions you'll need to deal with the joys of emulation, specifically DosBOX. But if you'd like an alternative, one gamer has found a way to get the whole thing going - in Java.
The creation from M210Projects is a reverse engineered source port of Monolith's original game. It follows the release of Blood Crossmatching earlier this year, which was basically a recreation of the original Blood, plus the Plasma Pack expansion, as an eDuke32 mod.
But if you already own the original and want to enjoy it without the added quirks of emulation, BloodGDX is for you. It's not a final release by any stretch of the imagination, but it works, and it's also a great reminder that Blood was criminally underappreciated and better than Duke ever was anyway.
For what it's worth, you can get the Blood Games for $3.98 in a bundle from GOG. The sequel is ... not great, but you'll more than get your money's worth out of the original.