Posting an update now that I'm farther through the Consular story.
It seems as if the planet
storylines were written with the Consular in mind from the very start. Playing this story (even after doing the factions on both sides 2 or 3 times) makes it feel like filling in all the missing pieces of a puzzle. While the JK is derping around chasing superweapons and Sith Lords, the SW is choking everyone to death just to make a girl upset, and the Trooper is being Garza's errand boy, the Consular
My suggestion is this: If the Consular is your 1st or 2nd character, put him off until you've experienced some of the other storylines entirely. That way you can appreciate just how deeply the Consular's storyline intertwines with the overall story.
The Consular story does suffer from a repetitive Act I and being a slightly weaker story in its own right, but it has the biggest "oh, so that's what was REALLY happening while I was here" factor.