XHTML 1.1 is intended to be used with the “application/xhtml+xml” MIME type. Yet almost no one does this, because IE doesn’t handle the “application/xhtml+xml” MIME type correctly, and draconian error handling is seen as being unfriendly to users.
If our site is stuck with the “text/html” MIME type, is there any advantage to using the XHTML 1.1 doctype over HTML4 or HTML5?
See this 8-year-old discussion of this very topic, which leads to this in-depth article. In short: there are disadvantages to doing so. Do not do it.
The executive summary, from the article: