I think you were right originally.
Let's just look at 2nd and 3rd harmonics for simplicity. A strong (above audible thresholds) 2nd, being an exact octave higher, is consonant, largely masked by the fundamental, and tends to add fullness or fatness. A strong 3rd, being a musical quint, or twelfth, lends a covered, nasal effect. At equal amounts, on their own, they sound quite different, and the 3rd, being further removed will be more distinctly noticeable. Which is more pleasing is subjective.