Q. What is the reason we take our teffilin off before our tallis?

A. Poiskim quote the Sha’ar Hakavonos (Tefilin Drush 5) and Sidur Hoarizal, who rule that one should not take off his taalis before the tefilin (Shaarei Teshuvo 25: 25, Kaf Hachaim 28: 9, Soles Belulah 25: 14, Machazik Brocho ibid., Kitzur Shulchan Aruch 12: 20, Yalkut Yosef 8: 5, et. al.). The reason given is that just like when you put them on, the taalis precedes the tefilin, and the tefilin are in their place only together with the taalis, when you take them off, you are careful not to leave the tefilin on without the accompanying taalis.

Horav Shlomo Miller Shlit”a further compared it to the extraction of two Sifrei Torah from the Aron Hakodesh, where the minhag is that the first Sefer is returned last.
Rivavos Efraim (O.H. 24) adds another three reasons; a) Since you have to place in the taalis bag the tefilin inside and the taalis toward the outside, so you will encounter next day the taalis first (O.H. 25), you therefore should take off and place in the bag the tefilin first. b) Since on certain days you have to take off the tefilin before the end of davening as in Rosh Chodesh before mussaf or in Chol Hammoed before Halel (minhag Ashkenaz) and you remain covered only with the taalis, you do so always. c) Poskim write that today many do not wear tefilin more than the time necessary since they require a clean body, a reason that does not apply to the taalis, we therefore take them off first and we leave the taalis on.

Rivavos Efraim further explains that there is a practical difference between the reasons given, and it is relevant to an unmarried shliach tzibur, that dons a taalis only for the honor of the congregation when praying before the amud. Whether he also has to keep the taalis on when he finishes davening until he takes off his tefilin, or he can just leave it by the amud, would depend on the above reasons.

Rabbi A. Bartfeld as advised by Horav Shlomo Miller Shlit”a