The Biur Halacha has an interesting chiddush (d”h yesh omrim) with respect to hidur. The gemara has a machlokes Beis Shamai and Beis Hillel whether to start with one candle and add more each night or start with eight and subtract one each night. Even though normally the halacha is like Beis Hillel against Beis Shamai, the M.B. suggests that this rule may be true only with respect to debates about ikar hadin, not with respect to hidur. The sugya continues that Rabbah bar bar Chana saw two elders, one who lit like Beis Shamai, one who lit like Beis Hillel, indicating that there was not a clear resolution. This is quoted by the RI"F, even though if halacha is like Hillel it has no relevance. It seems that since we are speaking about a matter of hidur, perhaps Beis Shamai's view is not totally rejected.
I imagine the sevara here is that when it comes to hidur, beauty is in the eye’s of the beholder. It’s not something that can be formalized as a matter of psak.
(In a comment earlier in the week GU suggested that the ikar takanah was hallel v'hoda'ah and lighting just provides a context for the brachos. Proof: if hadalakah was crucial, how could there be such a fundamental machlokes between Beis Shamai and Beis Hillel about how to fulfill the mitzvah? [By way of analogy, the Ran in R"H asks how there could have been such different views - shevarim, teru'ah, or shevarim-teruah - of how to blow shofar. It is impossible to imagine that there was no tradition of how to do the mitzvah.] In light of the M.B., the proof is a little less convincing. Perhaps because the debate was not about the fundamental ikar mitzvah, but rather only about a subjective element of hidur, there was room for a divergency of views to emerge based on different perspectives.)
R’ Shach in Avi Ezri writes that the takanah of mehadrin and mehadin min hamehadrin is not rooted in the din of hidur in kol hatorah kulah. Let me explain with an example: there is a din to take an esrog, and there is an added element of hidur in having a beautiful esrog. The person who has a $30 esrog, the person who has a $100 esrog, and the person who has a $175 esrog are all doing the same mitzvah, just each has invested more or less into it. Ner chanuklah is different. The takanos of mehadrin and mehadrin min hamehadrin are not just means of adding beauty to the same one takanah of hadlakah. They are actually three different ways Chazal instituted of being mekayeim ner chanukah, three different takanos if you will. (He has a number of proofs -- not for now).
I was wondering whether the M.B.’s chiddush would be true if you understand hidur like R’ Shach does. If the hidur we are talking about is not just a matter of beauty, the icing on top of the cake of the mitzvah, but is rather something that speaks to the very definition of how Chazal formulated the mitzvah, then shouldn’t we use klalei psak to determine that issue?