Our Gemara and Mishna on Amud Beis (Yoma 68b) teaches us a lesson about self-determination:

One who sees the High Priest reading the Torah does not see the bull and goat that are burned; and one who sees the bull and goat that are burned does not see the High Priest reading the Torah. The Mishna explains: And this is not due to the fact that one is not permitted to see both, but because there was a significant distance between them, and the performance of both of them is undertaken simultaneously.

Sometimes there is not a right or wrong choice.  People observing various parts of the service on Yom Kippur had the ability to choose freely which ritual to observe. The rabbis do not offer advice as to which choice is better, either because neither is better, or more likely what is better is subjective to each person.  Perhaps one ritual speaks more deeply to one person than another.

There are situations in halakha where the correct path is unknown and there is equal permissibility to either side.  For example, we have the principle of Judicial Fiat, שודא דדייני (Bava Basra 35a), and depending on the commentaries involve various degrees of judicial instinct or even whims (see Op. Cit. Ramban, Rashi and Tosafos.  Another example can be found regarding when to pray Maariv, which can be either after plag mincha or in the evening, which is codified in halakha (Berachos 27a, Shulkan Arukh OH 333:1).  An additional example is about the manner in which one stands or moves when praying, see Mishna Berura 48:5.

In truth, when we have a choice, is it really neutral or is there some subjective measuring rod we can use?

The Mishna (Avos 2:12) instructs, “Let all your actions be for [the sake of] the name of heaven.”  The Rambam (ibid) calls the reader to what he wrote previously in chapter 5 of the Shemoneh Perakim.  Namely, that every act, from the simplest physical act such as eating or sleeping, to the most spiritual should be with the intent of knowing God and growing closer to God.  The Rambam acknowledges that this “simple” idea could fill up pages and pages of sefarim, and take a lifetime to master, of which only a small few qualify.  It is important to understand that Rambam is discussing a different kind of Lishmah, not merely for a mitzvah’s sake but to somehow experience life in such a way that each act brings knowledge of God and therefore connection to God.

So to make a long story short, while there is no objective wrong or right in our Mishna over choosing which ritual to observe, the decision may rest on loftier ideas.  The person must decide which ritual will bring more awareness, knowledge and connection to God, based on personal circumstances.  I suspect, such situations potentially occur more often than once a year in the Temple.