In physics at least, a substantial proportion of peer-review goes via arXiv first anyway, so it's not really an either-or. In many cases, the real peer-review happens when people see a new paper in their area on arXiv, they send in comments or challenges, etc. to the authors, and in the best case, by the time a journal article is submitted for formal peer review, many of the relevant peers have already reviewed and helped improve it.

Some mathematicians have also gotten pretty active in using blogs and wikis for peer review and even actively doing research. I don't expect journals to go away, but I wouldn't be too surprised if there are some areas of the sciences where they become more of a formal archival service: where papers go to be filed on shelves once the real action/review/dissemination has already happened.