A lich sought out his condition, a vampire not necessarily so. So, a vampire might be more inclined to seek this for personal reasons, and it throws a little wrench at the party; Is it OK to stand by and let this horrible undead monster collect all of this power, presumably killing people to do so, if the end goal is fewer undead monsters?
on the other hand, a Lich might be better able to weaponize it. Spellcasters are often portrayed as being covetous of their secrets, and that sort of thing typically produces rivalry between peers. Perhaps if the lich was vying for superiority with another lich, he might seek out a way to bypass a phylactery (obviously something that should be destroyed in the climactic battle) and thus defeat he long time enemy.
In my homebrew a rebirthing chamber has been used by the mad* (rampant even) AI of an ancient crashed spaceship to endlessly clone the heroes and make stronger, evil-er versions.
This all came about when the new players started arguing over which PC would win in a fight. They asked me to come up with a set of duels to be run outside the campaign and I later folded the duels into the actual campaign.
* Really just subservient to the plague god.