Ronald, you are actually asking two questions here. The first has to do with traditional dulcimer styles and the second about modern, chord style players.
As Ken has explained, traditionally, the dulcimer was only fretted on the melody string and the bass and middle strings were left to drone. Many fine players still play in that style and achieve the haunting, ancient sound of traditional folk music. In that style of play, the tuning of the melody string has to change depending on the mode or scale on which the melody of a particular song is based. DAA and DAd are the two "major-sounding" tunings. Before the addition of the 6+ fret, DAA was the only tuning that could be used to play songs in what we call the major scale, so it was more common. The addition of the 6+ fret allows us to play that same scale in DAd, but as Ken mentions, if you only play on the melody string, DAA allows three notes below the starting note of the scale.
But if you play in the traditional drone style, you don't just keep one tuning all the time. The tuning is determined by the melody. In the key of D, Angelina Baker can only be played in DAA. Going to Boston can only be played in DAd. Shady Grove can only be played in DAC, and so forth.
Modern chord players who fret across all the strings and also have a 6+ fret can often (though not always) get those different melodies without retuning. But both DAA and DAd have exactly the same notes, so neither one has an advantage in that light. Rather the difference between the two has to do with chord voicings. Chords in DAA are more compact and chords in DAd have greater range, meaning the notes might come from two different octaves. But one is not better than the other.
At some point a few decades ago, dulcimers tuned DAd with a 6+ fret became a kind of standard for modern dulcimer players. That is how I play, but there is admittedly something rather arbitrary about it. Had most people tuned DAA when I started playing, that would probably be my main tuning.
Dusty T., Northern California
As a musician, you have to keep one foot back in the past and one foot forward into the future.
-- Dizzy Gillespie