In the gallery world, prints created using the platinum/palladium, wet plate collodion, and other antiquated processes generally fetch much higher prices from collectors than modern archival inkjet prints. These "craft" prints are desirable due to their unique beauty, archival qualities, and rarity. They are undoubtedly beautiful, but not necessarily more so than the best modern prints. And even though high-quality modern prints now boast upwards of 200-year archival quality, it doesn't really matter; perception is everything when it comes to the value of collectible art.
Some photographers--even outside of the gallery world--also consider these antiquated processes to be superior to modern digital processes. The common argument is that the old methods are more difficult, which in the minds of some, makes them more legitimate. Of course, the difficulty of any art form has never been tied to its ability to express emotion and move the viewer. It is also debatable whether the old techniques are actually more difficult to master than modern tools such as Photoshop, many of which require years of dedicated effort to fully master. Different than the old techniques? Yes. Easier to master? Not really.
I believe photographers should use whatever tools they enjoy that also enable them to fully express their personal vision. That might be anything from wet plate cameras from the 19th century to the latest iPhone apps from last week. What matters is not the tool, technique, or process, but the ability of the artist to capture an idea or emotion and convey it to the viewer in a powerful way.