For some, it's man with whip fights monsters in world of nightmare, Dracula may or may not be wearing a mask
For others, it's Ayami Kojima drawing elegant characters while Michiru Yamane composes beautiful music to set the mood, & IGA dictates story & aesthetic
For me, it's a combination of everything; gothic atmosphere that has thick ambience, with excellent tunes that'll stay stuck in your head long after you shut the game off, swinging pendulums with spike traps & medusa heads, creepy monsters mythological or original, and loose ties to real-world history. I'm OK with Dracula not being Turk-slaying Vlad Tepes to the T, this is a fictionalized version after all. I like how he's in an eternal struggle against mankind & God for his own losses. I like how he quotes from the Bible, "For what profit is it to a man, if he gains the world, but loses his own soul?" I like how Gabriel is essentially a Castlevanized version of Anakin/Vader, because I too like the story of Anakin/Vader (the rise, fall & redemption), as cheesy as the prequel trilogy was to some. I've learned to accept it, and while it's not the most original approach, it's still cool nonetheless. I like how he too is in an eternal struggle against mankind, God AND Satan.
People keep saying that a FPS Castlevania would be a dealbreaker for them, but they have yet to play Akumajo Dracula: The Arcade (pretty sure none of us has), which is the closest to FPS the series has gone, so how can you be 100% sure you won't like it? Some people love classicvanias, others metroidvanias over the classics, but I love both styles. 3D games are hit & miss but no matter what any of us say they ALL have their good moments. So I guess to sum it up, as long as they keep the gothic atmosphere/aesthetic in tact, memorable music, awesome enemies & good gameplay, 2D or 3D, i'm happy.
tl;dr Simon's Quest Tiger handheld is all i need