Bloodmage can be hard to quantify because he uses resources so differently. A newly minted Bloodmage has effectively 16 mana, which is only slightly better than the Sorcerer and doesn't come with the Sorcerer's excellent starting power. But that's not the best way to look at the Bloodmage.
His deal is that all health improvements are also mana improvements. Scaling effects like health powerups are effectively +1 mana. Health potions can be used as mana potions. Flat bonuses like the Pendant of Health can be worth staggering amounts of mana at the beginning, and trivial amounts at the end. Since no one doubts the Bloodmage's finishing power, this front-loading should be taken as a good thing. A JJ prep will give you access to a 36 point mana pool. This scales down with level, but remains useful until midgame, by which point you should have leveraged that pool into a comfortable position. If you work in a ding, you can routinely get a level 9 kill at level 5 (starting in at 4 and then dinging to 5 to refill and finish).
I do get what you are saying about the Bloodmage's relationship to B2P. All of the benefits I just described would work even better on a Wizard or Sorcerer who started next to B2P. Sure, the Bloodmage gets Sanguine, but I see that less as a synergy and more of a separate ability. To each their own.
EDIT: Forgot to mention something. The biggest edge with B2P is that it lets you ignore monster damage while still tapping your health as a resource. Sorcerer outperforms the Bloodmage against a monster that either of them can soak a hit from, but the Bloodmage has the option of attacking monsters that the Sorcerer can't even touch.