To the point of your question, I am not aware of any general guidance about whether the date of birth reported on a tombstone or death record is more accurate, especially for the circumstance of this case, as there seems a minor variance in the record between the two.
If there is any science or research to back up the notion that one is "better" than another, it would be interesting to see. I may have a little experience bias, but as with other conflicted information, I would work to weigh the research and information.*
Dates of birth and death are an important part of identity. Except in rare circumstance, it is hard to imagine that the difference of a few days between these sources would rise to the level where the identity became in question. Especially so here, given the facts as we know them, including that both differing dates are both made long after the fact.
A conclusion doesn't always require a date certain, either. In the, "is it really necessary to split this hair," there is nothing wrong with entering the birth as "1(or 4) May XXXX" [... or "4(or 1) May XXXX"]. In that case, I would cite both records by giving preference to whichever record I was reporting and noting the minor discrepancy with the alternative record that was in parenthesis.
Updated note: Learning that the two sources differ as to year of birth, you now have some "real meat" :-) to work with.
*That includes that I weigh what I know and don't know. Usually I don't know who supplied the information for a tombstone; only sometimes do I know who supplied the information for the death certificate. Even then I may not be able to weigh the informants credibility as to "date of birth."
If our birth record location clue is correct (from the death certificate; McLean County, Kentucky), then it seems unlikely a civil record of birth exists for dear Susan. According to n2genealogy, McLean County was formed in 1854; the county has marriage, court, probate and property records from that date forward. According to McLean County GenWeb, "Information and Photos," the "[McLean] County Clerk has birth and death records" from the years 1911-1949.
Trying to locate a baptismal record would involve yet other research.