If a feat has Draconic Heritage as a requirement, can it be taken by a character with the Dragonblood subtype, or does he necessarily have to take the Draconic Heritage feat?
No, they are not equivalent. Draconic Heritage gives the Dragonblood subtype (see below), but that is not all it does. Feats that require it as a feat could have just been written to require the subtype, but Wizards quite explicitly instead references the feat. You must therefore have it to take those feats.
Just a note on the feat. There are three different printings of Draconic Heritage, from Complete Arcane, Dragon Magic, and Races of the Dragon. The ones from Dragon Magic and Races of the Dragon are equivalent, and both give the Dragonblood subtype. The one from Complete Arcane does not, but it was printed before that subtype existed, and is otherwise identical so you should simply use the Dragon Magic or Races of the Dragon version if either is in play (since those are the books that use the subtype).
Anyway, personally I think this is pretty dumb: Draconic Heritage is a weak feat, and the Draconic feats that require it are also fairly weak, so I don’t see much reason to have to jump through all these hoops. Were I DM I’d just OK it. Probably wouldn’t even get hung up on the Dragonblood subtype either.