To me, a big advantage of Scala's "enrichment" over monkey-patching in Ruby or JS is that it isn't global. That is, you have to import the enrichment. Another code module in the program won't be unexpectedly affected by it.
In practice, I almost never use monkey-patching in dynamic languages because it's too dangerous. While in Scala there are cases where enrichment won't work, you can always just write a regular function in those cases, and there are lots of cases where enrichment _does_ work...