Both solutions have their place.
Canvas wraps, have issues also:
Mirrored edge? or wrapped edge. I personally do not like the look of a mirrored edge. So how to account for the portion of the image that will be wrapped.
Framing, most wraps are 1.5" thick, so this rules out most frames with a standard rabbet. Leaving only a floater frame and these are always more expensive.
Larger wraps say 30 x 45 and on up to 36 x 72 (largest I will wrap) require more time IMO than a similar canvas on gator. And the frame will need more prep time, with multiple bracer bars, both vertical and corner.
Tryptic style work, again is just more work, as you now have 6 edges that need some form of false image, either mirroring or other. If not too much of the image is in the wrap and your eye won't follow the image across the 3 panels.
If you are using an Epson, mirror edges are next to impossible on a larger print, due to the fact that Epson can't print canvas (at least none of the Epson's I have used 9880, 9900, and now 9000) without a enough skew error that your mirror edge will not line up, skew of 1/16 is OK, past this to 1/8 and you will see some of the mirrored edge in the face.
For larger prints, I will always will consider working with gator, as I can use any frame made with a 1/2 rabbet. For a multiple panel shot, again gator/canvas lends itself to this again as you can pick a very narrow metal frame or wood frame and keep image continuity much better.
Coated gator prints, are more durable, period. So for an institution, like hospital or office building where there is a lot of traffic, a framed gator print will possibly be a better solution.
Gator prints also take the cost down as I no longer have to job out the chop/join of the frames, not as much an expense but time consuming.
Paul C