Having run through the story twice, as a DS Sage and an LS Shadow, I honestly preferred the LS path. It just felt more legitimate/realistic, especially since the DS options for your quest feel more like "I'm a vindictive murderer that is willfully killing you rather than saving you", and it does seem kind of odd that you get lauded and (spoiler) placed on the Jedi Council if you're oozing Dark Side and killing people rampantly, unless you're using some kind of outside justification not really supported by the written lines (the justification most often used is "you may be evil, but you're evil working for our purposes and working within our guidelines" or simply assuming that the people you're reporting to trust your answers implicitly and never bother to check or even wonder why so many people you seem to encounter just end up dying in a continual string of coincidences and failed attempts at redemption/conversion).
To enjoy the Consular story, you have to enjoy the world building and development of side characters more than or as much as running around killing bad guys and doing awesome adventure-y things. The best comparison would be that the Knight story is like KotOR 1 (wherein you play Revan, running around doing awesome things, with an explicit and well known villain right from the start, and your companions are really just there as color on your path to awesomeness) whereas the Consular is more like KotOR 2 (wherein you play the Exile, spending most of your time dealing with problems with complex solutions and outcomes, moral dilemmas, and NPCs that are more than just scenery, not to mention always fighting a "mystery evil" that you're not even sure who it is or what they look like until you finally confront them/force them to reveal themselves).
The Knight is, explicitly, a warrior, and their story follows that vein quite closely; the Consular, on the other hand, is a diplomat, a teacher, a secret keeper, and an investigator. It's a much more complex job description and, as such, requires a story with more mystery, lore, and world building than the action/adventure of the Knight story.
Personally, I loved the Consular story and preferred it over the Knight one. The Knight felt more akin to being told to "go hunt down X" over and over again. It was just a continual series of explicit commands. The Consular quest seemed to provide a story with much more open ended and complex problems (Jedi Masters are going crazy throughout the Republic; figure out the cause and solve it however you feel is best for Act 1, diplomacy and mystery for Acts 2 and 3). Of course, the fact that you ride at the head of 3 personal armies of elite ***-kickers at the end of the story probably helped a bit (although you don't actually get to see any of said armies, except for their leaders).
The Consular story is strange in that, unlike most of the other stories which are either love-it-or-hate-it or largely considered to be mediocre, the Consular story runs the entire gamut of utterly despised to favorite overall story, which is one of the reasons why it's so hard to explicitly pin down. It's definitely got elements that some people won't really like (the companions definitely take some getting used to since you get a *single* Force user who is a bit saccharine for some peoples' tastes, though the "slow" progression of the story and lack of major confrontation right from the start often come up), but it's also got some that, what I will call, a more "refined" palette will appreciate more (mystery, diplomacy, world building). It's hard to say with any accuracy whether a person will or won't like the Consular story. It's just one of those things that you have to try out to see if you like it or not.