Canvas prints, sometimes also called Canvas Giclée, are very similar to traditional pigment on canvas paintings. So any time you're trying to fit into an "old world" type of environment, they are a very attractive option. The traditional stretched option lines up well for framing just like an old painting would, and the gallery wrap options mimmic more modern applications of canvas by painters. Plus the newer "thin wrap" style of canvas gives a smaller and lighter hanging/mounting option, while preserving the traditional canvas look. (In theory I suppose you could say it's comparable to the old masters that glued their canvas to planks of wood before painting them... so we've gone full circle.) I should also note that there are places that will transfer emulsion onto canvas as well, printing on paper, then wet stripping the emulsion layer and bonding it to a layer of canvas.
As ahockley noted, the ink bleed from the printing process can sometimes lower the sharpness of the image, so this shouldn't be used if you have to have an absolutely razor sharp image, especially up close or for a small print size.
Metal prints have a very industrial feel to them. One of the first places I've seen these become popular was in shops and garages of racing folks. When you think about it, they're very similar to a car body panel... thin metal (usually Aluminium) with a layer of image (special dyes instead of paint) covered by top coats of clear protectant (pretty much the same stuff the high end car painters use). In the US, BayPhoto are the masters at this IMHO, I have a few here in the house from them, have seen a number of them, and have sold a couple.
They generally are "ready to hang", you take them out of the box and put them on the wall. No framing, etc needed. Combine that with the very sleek industrial feel and they're quire popular with a lot of folks that don't want the same old same old.
There are a number of finishing options with metal prints, but to me, the "prototypical" example is the high gloss finish. This really gives a huge pop to high contrast images like fireworks, or deeply saturated images.
Another alternative "media" you didn't mention is Acrylic. fotoflōt do these very well. It's kind of like the float mount metal prints above, in that it's a sheet of acrylic with your photo bonded to it and the edges laser cut. They have an additional flair in that the acrylic then is mounted to the wall with magnets. Now, having said all that... it isn't really an alternative media. At best it is alternative mounting/framing/presentation... as it involves printing on traditional emulsions on paper first. Then bonding that to the acrylic. But really, you'd never know it to look at it, and everyone seems to consider it a media. Personally, I don't own any fotoflōts, but the ones I've seen have really looked great, seemingly no mater what the image was. If it looks good printed it will look good mounted that way.
A forth option, and I can't believe I didn't think of it before: duratrans in a lightbox. I believe DPI-SF does the lightboxes at our HQ building, which includes a number of amazing lightbox images. This makes for literally glowing images. I'm not sure exactly what would be the ideal image profile for this, but lots of stuff seems to look good so far. (There's another lightbox at HQ that's even better than those three, but I can't seem to find a shot of it online.)