It is not as well known that there are many reader-friendly editions that present these cantillations in conveniently separated form. (BHS, like the great Masoretic manuscripts, presents both cantillations superimposed on a single set of letters. Because BHS and editions close to it dominate the market, alternatives are not well known.)
One might think that the superimposed presentation poses only a mild inconvenience if all you want to do is pronounce rather than chant a Decalogue. In other words, one might think that there are just more accents to ignore than usual.
While this is largely true, it is not 100% true. The few words for which it is not true remind us of the ways in which cantillation interacts with pronunciation in all of the Hebrew Bible, not just the Decalogues.
Perhaps the most obvious words varying in more than just accents are the two words varying in vowel marks. One is על־פני, which, in superimposed form, looks like this:
What the heck? That poor nun is burdened with both a qamats and a pataḥ?! The other such word is מתחת, whose tav is similarly burdened:
We could dismiss these words as, while differing in more than just accents, still not differing in pronunciation. That is another statement that is largely true but not 100% true. There are some remaining communities who pronounce qamats and a pataḥ distinctly.
A word whose pronunciation varies between cantillations in all communities I'm aware of is כל־מלאכתך, which, in superimposed form, looks like this:
Again (but for a different reason) I feign surprise by saying: what the heck? Assuming we even remember what rafeh normally means, what the heck does it mean when combined with dagesh?! Here it may help to see the cantillations separated rather than superimposed. I provide those below, along with some phonetic transcriptions using Jacobson's system:
(Those transcriptions are part of a wider project I am working on to provide transcriptions of the entire edition of MAM used in the Al-Hatorah Mikraot Gedolot. At the moment all that's available is the rest of Exodus 20.)
That's all I'll write for now on this topic; if it stirs up some interest I may present and discuss a few more Decalogue words whose pointing differs by more than just accents.