Blood+ Adagio is a prequel to the anime series, with Saya having just woken up from her first hibernation. It's sometime before the events in the flashback that Saya had in episode 17, before the Vietnam war and Saya and Haji are already working with the Red Shield.
Diva and co have already made human chiropterans this early on. Chiropterans were actually made, with the intention of creating chevaliers, . It also shows more of how the drug, Delta 67, was being developed in its very early stage.
It's actually created before the anime and by a different person than the anime, but it still
closely precedes the events in the anime. It has a different form, it's lighter and more optimistic than the anime. Saya was drawn different, and for a manga this short, it had too many characters! The characters suffered and weren't given more time, everything felt compressed. It would've been better if it was another episode, or added to the anime as a flashback as I thought it couldn't really stand alone. It didn't really give any more information
The author wanted to infuse Russian culture too much, I thought more time was devoted to creating the setting rather than focusing on the story and characters. More thought was put into the character designs and Russian nobility in the 19th century, it would've worked but it shouldn't have been at the expense of the story.
I would still recommend this to those who have watched the series, especially those who like Saya/Haji pairing. There was a continuity error, basing on the anime, this should already be after the time when they've made their "promise", but it doesn't look like they've made their promise here yet. I liked it better here though, they were younger and more optimistic which I thought was more believable because Saya's mission was easier to do here, things weren't on as large a scale as they were in the anime. It would've been nice if they revealed more about why Saya needs to hibernate (I still think it's so unnecessary to have them hibernate that long) but I really liked the ending