The first two mishnayos in the perek establish 2 rules: 1. Something which is more common (tadir) comes before something less common. 2. Something with a higher level of kedusha comes before something that has less kedusha. The gemara then raises the question whether the advantage of tadir is greater than mekudash or the opposite, and fails to prove one way or the other. As a result, the Rambam (Temidin U'musafin 9:2) paskens that one who has tadir and mekudash in front of him can choose to do whichever he would like to do first. The Taz (O.C. 681:1) writes that since the gemara doesn't reconcile which is better, we should assume that the tadir advantage is greater since it is a general Torah principle. The Taz means to say that the concept of tadir is learned from a pasuk 89a whereas the concept of mekudash seems to just be a sevara. However, the Sha'agas Aryeh (28) rejects the Taz because the concept of mekudash is also derived by the gemara in Horiyos 12b from the pasuk of vi'kidashto. Furthermore, the Sha'agas Aryeh says that the Taz seems to have missed the Rambam who considers tadir and mekudash equal to one another.
Based on this the Sha'gas Aryeh struggles with the Shulchan Aruch (Hilchos Tefillin 25:1) who says that after putting on a Talis with tzitzis one then puts on their tefillin because of מעלין בקודש. How can the Shulchan Aruch use the concept of ma'alin b'kodesh - that only applies within one mitzvah, but in terms of prioritizing two separate mitzvos the more mekudash thing comes first (his question is based on the premise that tzitzis which is not an obligation would only qualify as matzuy, and therefore doesn't have the advantage of Tadir to consider it equal to tefillin)?
The Sha'gas Aryeh approaches this by saying that tadir and mekudash are only rationales to prioritize one mitzvah over another, but when one thing is considered only a d'var ha'reshus, not a mitzvah, there are no rules about what has to come first. Since tzitzis isn't an obligation we regard it as a d'var ha'rshus and there is no requirement to do tefillin first.
Another approach to answer this question is offered by the yad ephraim in his commentary to Shulchan Aruch. He explains that the rationale of מעלין בקודש is only be used to be machriah between the two equals, tefillin which is mekudash and tzitzis which is tadir. The concept of מעלין בקודש is on the individual. Since there is no preference between the tefillin and tzitzis using the mekudash and tadir concepts, we apply the מעלין בקודש to say that he should move himself up from a lower kedusha (tzitzis) to a higher kedusha (tefillin).