Sorry for bumping this thread from last week.
ubiquitin wrote: “This is why it is the generally the weekday tallis (worn more often and usually for longer time) that is used to wrap a nifter which he “wears” in the olam haemes after having worn it for years in this world.”
I cannot say what is “generally done” but the Nitei Gavriel brings down that some say the shabbos tallis and some say the weekday tallis. (Hilchos Aveilus 47:10)
http://hebrewbooks.org/pdfpager.aspx?req=46539&st=&pgnum=241
He also states that in EY, they carry the meis with his tallis do not bury with the tallis. (Hilchos Aveilus 47:7)
http://hebrewbooks.org/pdfpager.aspx?req=46539&st=&pgnum=240