well for one, we actually get to know the character that becomes Dracula. He isn't just a 2 dimensional footnote in the manual of the game who shows up for a few minutes before the final boss and then leaves after a grand speech about his woes and miseries and how he curses God for shit.
With all due respect, personally, I didn't get to know him any better than Mathias, who was in the opening narration besides the booklet and ending. Patrick Stewart told us almost everything about Gabriel through narration, as well (poor, poor Gabriel, etc, etc). His relationship with his wife wasn't any better established. All I saw was a vengeful dude who thought he was being a hero, and then decided to be Dracula. With LoI, the Belmont clan was established through Leon, whom we really saw develop from a impulsive and naive knight who thought he could tackle any foe (used to having Mathias cover him with his tactics), to someone who sees his limitations and pledges to overcome them with the help of, and for the additional sake of, Rinaldo. He rescues his wife only to see her turned into a vampire and then sacrificed to fight the evil that has cursed them all. As I'll mention in a minute, this served the dual purpose of establishing Dracula, too, through another's eyes.
The parallel of losing his wife as Mathias lost his, and yet refusing to join his friend in his grief and revenge establishes the Dracula/Belmont rivalry pretty well in the social-historical background of the Crusades and pseudo-science/magic of alchemy, even if unconventionally, whereas the unconventional stories about the Lords of Shadow and the devil and the Brotherhood of Light in a unclear fantasy timeframe all seem like an origin story for something other than Dracula or Castlevania. LoI's story establishes Dracula's origin character as a man who not only served and was betrayed by what he felt was a holy cause, but had the background of a commander and a dabbling magician/alchemist, which fit into what we've seen with the Castelvania world's Dracula over the years in-game and in text prologues. In this indirect manner, through a Belmont's eyes, it established a Dracula better than Gabriel's Dracula, who has an abrupt turn after you've played him pretty clearly as a hero throughout the game. A tortured, manipulated hero (manipulated by some kind of mask no less), but a hero all the same. The turn to the Dark Side doesn't hit me right.
LoI just worked as a better "Castlevania" origin story for me. By the end of the in-game LoS (pre-DLC) we don't even have a full turn to Dracula or the impending conflict, except a bizarre future scenario where Dracula is going to fight the devil. Additionally, from a Castlevania standpoint, LoI helped serve up some origins for the weapons hidden around the castle from fallen adventurers and the villain's "game," established Medusa, and had some characters of interest such as Joachim and Rinaldo. Rinaldo in of himself, and how his daughter's tragedy fit into the story, was more compelling than any narrative element of LoS. But I'm rambling now.
Those are just my thoughts. Everyone is entitled to their own opinion, but all I'm saying is I don't think it's as clear-cut as people make it out to be. And we can all talk about how IGA's stories tended to have some "emo" in them, but LoS is incredibly angsty and melodramatic, and not in a sympathetic, endearing way. Particularly with what they've been trying to sell in MoF's newer trailer.
Plus, LoS is missing that moment of triumph: "I'll hunt you and the night!"
Well, how about that new LoS2 trailer soon...