Yes, it's fine. It's got changes to voice acting and a few minor things to make note of, like playable Maria and whatnot. You have to delve into Dracula X to unlock SotN, but it can be done relatively quickly if you grab a youtube vid as a guide.
SotN is my favorite game of all time, so if anybody would be overly-critical about differences between SotN versions (ex: the way people get hyperbolic about which version of Final Fantasy 6 people are allowed to enjoy), it would be me. I'm not though, so that should tell you that it's perfectly fine.
I have the utmost nostalgia for the original's voice track and untouched state, but neither is better or worse, and the only thing to really consider is that SotN on PS1 is a smaller filesize than Dracula X Chronicles... but Dracula X and the unlockable Rondo of Blood are fine game to have.