I saw a video with this chord and thought it was an Amaj6/9, but a lot of the comments are calling it an "Amaj7 add13" or "Amaj7 13(add 9)." I'm not sure how the notation works here and was wondering what the difference between those labels and what this chord should be called are. Thanks! Image Caption: Notes from bottom to top: A, E, G#, C#, F#, A, B
Dominant 7th chords will always have m7 (root to m7 note), and be called simply '7th' chords. Whereas major 7th chords (with root to M7) are always named 'maj7'.
So, your header "13 or 6/9" is a bit of a red herring. As an A13th chord, (a dominant) it will need G♮ as its 7th, and certainly F♯ (13th)in it. Whether it will contain ^9 and/or ^11 will often be up to the discretion of the player.
The other option of an A6/9 chord must contain ^6 (F♯) and ^9 (B). Making it quite a different beast.
With C♯ it's obviously a major chord, so that part doesn't need noting. The G♯ makes it maj7, The F♯ could make it 6th or 13th, and the B makes it maj9. Putting that lot together, Amaj13 sounds reasonable, or more precisely Amaj13(omit 11).
Amaj7(9,13) is the most accurate description of this chord. Amaj7 13(add 9) is also acceptable.
This chord with A as the root has a G♯; it therefore is no mere Amaj6/9. It has to be at least Amaj7.
This chord with A as the root also has a F♯ (at least) a 13th above the root. Calling it a 13th chord is therefore more accurate than calling it a 6 chord.
This chord with A as the root also has B as its topmost note, more than an octave above the root. It therefore is also some kind of 9th chord.
Calling it a mere A13 chord implies it uses a minor 7th instead of a major 7th, even though that chord symbol can also include the 7th and 9th.
Therefore, the most accurate chord symbol for this chord is Amaj7(9,13).