Is the answer to this question simply that both of these concepts aid in understanding which chords and intervals are consonant or is one of these discoveries actually better than the other?
As the "rules" for handling dissonance seem (to me) to be a bit convoluted, I think it's easier just to use a table of intervals. Historically, intervals were classed into three broad types.
Perfect perfect consonances (no major or minor form): unison, octave, fifth, fourth*
Imperfect consonances (major and minor): thirds, sixths
Dissonances: (major or minor) seconds, sevenths, all augmented or diminished intervals, *perfect fourth against the bass note but not against upper notes
For counterpoint (especially between bass and melody in popular styles) this seems about detailed enough. There have been lots of attempts to classify dissonance and consonance through auditory measurements; none seem to agree exactly with musical practice.
Ludmila Ulehla's book, "Contemporary Harmony" lists various chords as to their dissonance intensity; she also discusses how this has changed.