BLM/RDM is arguably the "DD" BLM. (Melee reference: WAR/SAM)
With "Fast Cast" giving you enhanced casting speed and slightly lowered recast timers, you can fire spells off faster. Refresh and Convert will play a huge role in sending your damage "up, up and away!".
You'll have the resources to keep yourself alive (Gravity, Stoneskin, Blink, Aquaveil, Phalanx, Mana Wall + Convert), but lack many "PT friendly" spells.
BLM/SCH is the "utility" BLM. (Melee reference: WAR/NIN)
You'll be able to the same damage you would as /RDM, in shorter bursts, but to do it in a shorter amount of time you lose out on DoT (damage over time) due to lower MP recovery (shouldn't be that big an issue inside abyssea, though I still manage to burn my MP dry when I want).
You'll have the resources to keep yourself alive, but you'll have to be out of "Dark Arts" to do them (decently well at least). You'll have access to some "PT friendly" spells, like "ghetto Curaga II" (Accession + Cure3) or status ailment removal (-na's/Erase).
You'll do a lot of bouncing from one art to another if you're aiming to make full use of both sides of /SCH.
BLM/WHM is the "support" BLM. (Melee reference: WAR/PLD)
You'll have no "Fast Cast" or "Casting time-" from /WHM and you'll sell your DD capabilities short. You'll still be able to push out some punishing nukes, but your DoT will drop drastically compared to /RDM and /SCH's that are going all out.
Your role /WHM should include Hastes, status removal (-na/Erase), "backup" cures. You won't "need" to burn stratagems to use this SJ to it's fullest (mostly because they won't exist for you). You'll have some decent self-defense (akin to /SCH) and you'll have a more "PT friendly" role.
BLM/BRD is the "proc ***" BLM. (Melee reference: WAR/Nothing)
You're there to get Green/Yellow/Pink/Whatever colour you want to call it. When you find the element, you nuke as much as you need, then ES -> Threnody if you still don't have it.
Your nukes will be laughable, but they'll get your job done. For more chances at landing Threnody* /BRD, you'll want to load up on Magic Accuracy+.
EDIT: * landing Threnody without the use of Elemental Seal