The difference from my experience is that certain DTDs switches the browser between quirks mode and strict/compliance mode. If you need backwards compatibility you would use an older DTD to force the browser into quirks mode.
If the strict/compliance mode is available in the browser, if you use XHTML strict it forces the browser to comply to standards. If most cases you wont notice it but when you get a 'quirky' problem the DTD can be an issue.