Just gonna copy and paste my comments on why the N64 games are the best of the bunch.
TLDR: By trying to define what constitutes "Castlevania", I use three criteria; high-commitment platforming, limited combat and gothic / horror atmosphere. The N64 games are the only ones that satisfy all three appreciably.
In my opinion, Castlevania, or at least Classicvania, can be boiled down to three distinct elements;
High-commitment Platforming:
Setting aside Metroidvanias, no Castlevania protagonist could ever be accused of being fast nor graceful. You generally have one speed (angry walk) with no momentum and very little if any control over your character any time their feet leave the ground. Platforming in Castlevania is so much less forgiving than its peers that you can't help but hold your breath until you reach the other side, even for stuff that looks fairly safe.
Limited Combat:
You have a whip with a relatively short range and with few exceptions, it only attacks in one direction (and it's worth pointing out that the difficulty level of the games with multi-direction whipping is much lower than those without). You have a few sub-weapons which grant you a longer range (dagger and cross) or vertical reach (axe), but for the most part you're fighting enemies when they're close enough to affect you, and they often have you at a disadvantage in terms of positioning. Enemies also occasionally have more speed and mobility than you (Medusa Heads and Fleamen especially), but rarely take more than a single hit to dispatch, so even if you're not moving through the game quickly due to the intentionally slower pace, you're still generally moving forward without spending too much time on the rank and file baddies.
Gothic / Horror Atmosphere:
Castlevania is all about spooky forests, dark graveyards, crumbling castles, haunted swamps and eerie caves. Menacing eyes watch you from the shadows. Stages are foggy or stormy and rarely lit by anything but flickering candles and moonlight. There's corpses and ghastly statues everywhere. The enemies you meet are literally spawned from hell, and the bosses you encounter often have deep literary or even mythological context.
So how do those apply to the 3-D Castlevania games?
Right off the bat (lol), Lords of Shadow is out. The platforming, if we can really call it that, is mostly "hit button when sparkly thing appears to auto-attach whip" with a dash of "press button to grab ledge." Very rarely are there legitimate platforming segments. Likewise, the God of War-esque combat has you just flailing the whip around, executing multi-hit combos on multiple enemies at once. I'm not saying it's bad, but it's not Castlevania. Likewise, Lords of Shadow plays a little loose with the setting; Agharta and Pan's Temple are just too brightly lit and feel like something out of Lord of the Rings, and I'm not even gonna talk about the city setting in LoS2 (that said, the actual castle sections in Lords of Shadow are amazing).
Lament of Innocence has very little platforming as well, and the combat is similarly full of enormously flashy, multi-hit, room-wide flailing whip attacks. Nails the atmosphere, though.
Curse of Darkness, as far as I can recall, has no platforming to speak of. The combat is a little better, being more melee-oriented due to the character not using a whip, but it's still very heavy on whacking the shit out of enemies for a while until the explode. The atmosphere was alright (though for large stretches it tends to feel very generic).
And then you get to Castlevania 64 and it's "expansion pack", Legacy of Darkness. There's a ton of platforming going on here, and none of it is of the 'automated' variety you find in the above games where you're just pressing a button to 'snap' to an object. You're making jumps across moving platforms, shimmying down cliffs, the whole nine yards; legit platforming. Combat makes a similar transition; the whip is extremely narrow and while there is a lock-on feature, it actually feels like a 3-D version of the 2-D gameplay. Similarly, the game's atmosphere is fantastic, full of dank waterways, haunted hedgemazes (with a legitimately scary enemy chasing you through it), spooky villas and plenty of Castlevania locales (the clock tower is especially memorable).
That said, there's a ton of legitimate issues with the game; annoying puzzles (The Magic Nitro/Mandragora bit especially), a plethora of bugs, some odd design choices (motorcycle skeletons!) and an especially awful camera. But considering this was the transitional era from 2-D to 3-D some growing pains are expected, and despite those issues the game still manages to absolutely capture what I consider the essence of Castlevania to be and move it into the third dimension, in a way that the later 3-D games simply haven't. That's not to say they're bad games by any stretch (in fact, they're quite good), just that they're not really carrying the spirit of the series forward. At worst, they're simply character action games with a healthy coat of Castlevania paint applied. But you really do have to go back almost 20 years to find the formula's best 3-D outting.