Question: Why do we not wait for a Tallis to come if one only has tefillin but we do wait until Motzei Shabbos, Saturday night to say Kiddush Levana?
A. The Shulchan Aruch and Rema (Orach Chaim 25:1) says that you should put your Tallis on before your tefillin in order to go up in levels of holiness in this way beautifying the mitzvah. However if one doesn’t have the Tallis with him at the time but knows its coming he should not wait to put it on but rather put the tefillin on first and then the Tallis later. The Magen Avraham (2) explains that though one is sacrificing the beautification of the mitzvah but one shouldn’t push off the mitzvah of tefillin lest he loses out on putting it on in a timely fashion, for a mitzvah done at the right time is more beloved by Hashem.
B. The Rema (Orach Chaim 426:1) says we should push off the mitzvah of Kiddush Levana until Motzei Shabbos (as long as there is no prolonged concern of overcast) in order to beautify the mitzvah by doing it at a time when we are feeling more joyous, dressed in fancy clothing. (Truth is the Mishna Berura (20) brings many Achronim who say one shouldn’t delay the mitzvah of Kiddush Levana, but there seems to be a contradiction in the Rema that must be resolved!)
C. What aspect of the mitzvah is being beautified in each case?
Answer: By kiddush levana the beautification is on the mitzvah itself to dress nicely when saying it but by tefillin and tallis it is only a side issue of what comes first to treat the holier one with more respect.