I've always been wondering about this myself. Although many people disagree with me I think the Consular story isn't that bad (although I've only just started a Jedi Knight) - it does start off pretty slow but IMO by Chapter 3 the Consular becomes in many ways a lot like Satale Shan, you know?
But the two Advanced classes are very different from each other in many ways, and here's my opinions.
Reasons a Sage makes more sense:
-You train as a padawan with a single-blade training blade, and then craft a single bladed lightsaber at the forge. It seems a little weird that you would make that single lightsaber only to ditch it for a double-bladed one so *quickly* after reaching level 10 - unless maybe he just modified it accordingly after choosing his path on Coruscant?
-Qyzen & Nadia will sometimes specifically mention healing when low on health. It seems odd to me that Nadia would say "I can't heal this myself" if you're a Shadow and can't even use healing abilities besides Meditation (which you can't use in combat anyway).
-(I think) Sages are technically stronger in the Force than Shadows, which fits your Consualr's exceptional power - Shadows seem to focus more on psychic mind-based Force abilities rather than telekinetics (which you use at several points).
-Wookieepedia's descrption of a Jedi Consular is pretty much the same as a Sage in the game - Shadows are described as being more like specialized Jedi Knights.
Reasons a Shadow makes more sense:
-From what I know Sages don't really go on adventures the way you do in the game - rather they're more diplomats, healers & teachers. Which IS a big part of your storyline...but Shadows have much the same kind of philosophies, they're just more trained in combat and take on more active missions.
-IMO 90% of the non-class-specific missions (which you will need to do to level up) fit a Shadow better as they often involve going into compounds, taking out a named threat, etc.
-Also there ARE a number of points in the JC story that do feel a lot like things a Shadow would do (Coruscant, Nar Shadaa, and the spaceship missions most notably).
-Nadia uses a double bladed lightsaber as well, though she isn't really a Shadow as she does lack the stealthing abilities that give Shadows their name. But since you are her master - maybe you could've trained her in the use of a DB saber, or maybe she wants to be just like you?