Canon is never as absolute, definitive, or rigid as many fans seem to think. It's not some formal policy handed down from on high; it's just the current creators' assumptions as to what parts of the franchise's past they choose to consider "real." So the definition of canon changes all the time, and tends to reflect whatever the most recent interpretation is. For instance, on Dallas it was canonical that Bobby Ewing was dead until the producers decided to say it was all a dream, and then that entire season became non-canonical. In Trek, first it was canonical that the Borg had no interest in individual life forms as a rule, only in technology, but later it became canonical that all Borg drones were assimilated humanoids. First it was canonical that Data used contractions routinely, then it became canonical that he never did. And so on.
So generally newer canonical assumptions supersede older ones, which would suggest that the new FX should be considered to take priority. Of course, ultimately it's irrelevant unless some future Trek producer specifically decides to revisit, say, Flint's mansion or the Tantalus Colony and has to decide which design to use. But that's unlikely, and they'd be just as inclined to create some new design of their own.
I mean, which of the many inconsistent depictions of the planet Vulcan or the skyline of San Francisco is canonical? Which of Saavik's or Zefram Cochrane's or Tora Ziyal's faces is canonical? They all are. A canon is a series of fictional works that pretend to represent a consistent reality, but since they're fictional, that reality is subject to reinterpretation in the individual stories. Canon is not defined by the specific details, but by the overall whole. Creators of new stories keep them consistent with the general shape of the universe as defined in the past but are free to reinterpret details to suit their individual needs or creative choices.
So it's really not a meaningful question. Star Trek, the overall television series, is canon. Differences in how its visual details are rendered onscreen have no effect on that. I mean, think how many contradictions there were within the original unaltered episodes. In "The Enemy Within," neither Kirk had a uniform insignia at beam-up, but then they both did before they had a chance to change. Was that a canonical detail, or was it just an inconsistency in the production of a work of dramatic fiction? Or what about the shots of the Enterprise where they used stock footage from the second pilot and the nacelles suddenly gained spires and lost their rear domes? What's canon is the overall narrative, and the details are always subject to interpretation or change.
But as for which designs the individual fan would choose to consider "real," to me it makes sense to go with the new versions in Remastered. After all, most of the shots that were replaced were stock footage that was only a crude approximation of what they were going for anyway. I mean, why believe that Flint's mansion "really" looked like the Rigel VII fortress, right down to the same coastline and the same planets in the sky? Why believe that the Tantalus penal colony looked just like the Delta Vega lithium cracking station with a few modifications? Why believe the Aurora looked like a Tholian ship with Starfleet nacelles stuck on by Klingon battlecruiser wings? I don't think it makes sense to take any of those visuals literally. They were just the best approximations of the intended reality that the production crew could manage with limited resources. The TOS-R versions are probably a better reflection of the intent of the original stories.