From what I've seen of all the different versions of SotN, it seems like there is no single "definitive" version of the game. Every release has its own strengths and caveats, which I've chronicled here in my own personal order.
1. PSX Original (CRT)
+Originally designed for the PlayStation
+Sharp even pixel sizing on a horizontal and vertical plane (no dither or shimmering effect when scrolling)
+Basically the most cycle accurate way to play the game
-Lacking the extras some of the other versions offer, no voice language option
+/-? Laughable original dub track
2. PSP digital "PSOne" release (w/ CRT connector)
+Nice even pixel sizing
+Decent screen sizing options
+Custom scaling engine that preserves the pixel sizing no matter how you scale it
+Authentic 240p presentation in interlacing mode
-Added dither on an LCD panel
-Pixel edges are a tad softer than PS1 (invisible to CRT displays)
3. PS3 digital download ("PSOne" release)
+Essentially identical to the PSP with even pixel sizing
+Accurate Moon glow effect under Dracula's Keep
+Preserves the original aspect ratio with no screen sizing options (albeit a stretched mode)
-Softer pixel edges even with "Smoothing" turned off
4. PS4 "Requiem - SotN and Rondo of Blood"
+Sharpest pixel output available on consoles
+Proper horizontal pixel sizing as long as you pick "Full Mode" (-the smaller "Normal Mode" oddly displays short square pixels)
+High resolution 3D backgrounds/objects
+Dracula X Chronicles' extra familiars and items
+Rebound Stone and Save Room coffin jagged lines anti-aliased, really a personal preference
-Despite the higher resolution textures, the 3D objects in the game retain their PS1 era janky 3D animation
-Performance based on the slower PAL 50hz Dracula X Port, though it maximizes performance wherever possible, despite this it shares some of the downsides of that version such as sound issues and saving/loading stutters (likely the result of a quick and dirty PSP conversion)
5. PS Vita
+Sharp pixels
-Uneven 256p horizontal sizing (the original displayed at 240p)
-Custom sizing is available but the forced touch controls make pixel perfect sizing impossible
6. PS3 with original SotN PS1 CD-ROM
+Sharp pixel count
+Proper scaling
-Uneven pixel sizing resulting in shimmering issues
-Inaccurate effects such as the moon glow in Dracula's Keep
7. Xbox 360 Arcade (by Digital Eclipse)
+Backwards compatible with Xbox One
-Uneven horizontal scale (screen sizing is available)
-Pixel perfect scaling virtually impossible
-Enhanced mode smooths over pixels and displays by default
-Permanent borders
8. Dracula X Chronicles PSP version
+Saturn familiars and items
-Blurred art assets
-Broken vertical scrolling
-Inferior sound effects
-Permanent borders
9. Saturn
Really more of an alternate option but still has major issues
+Richter and Maria unlocked at the start
+Original moveset for Maria not seen in DXC or Requiem versions
+Two original areas, new bosses/music
+New familiars and items (carried over to the DXC and by extension Requiem versions)
-Massive slowdown
-Missing transparency
-Stretched 320p resolution with heavy aliasing
-Pause menu loading times
-The map (arguably what you'll be accessing the most) is IN the pause menu
10. PS TV
-Cannot run in 1080i, only 720p or 480p
-No video options (unless using custom firmware)
-Blurred art assets
And that about wraps up my exhaustive analysis. Let me know if you want me to do any other games with a ton of versions!