The intervals created are a major 3rd, minor 3rd, again major 3rd, perfect 4th, major 3rd, minor 3rd, major 3rd and finally a perfect 5th. If we interpret these as chords it could be A, G#m, F#m but for the F#m you're only playing the 5th, first inverted (below the root) then above the root (first F# is when you both play fret 11, second one is the last note; guitar 1 is playing C# one octave above from the first time it played that same note).
So... you start with the 1st degree of your key, then you play the 7th degree which is one of the dominant degrees, it "wants" to become the root, so it creates tension. You go back to the root, resolving the tension, and then you move to the 6th degree which is a direct substitution, it's stable, so no tension there. Back to the root, and then you create tension again with the 7th degree, then back to the root and 6th degree to resolve that tension.
If you only play one of those parts by itself, the hint about the scale on which it is goes away, and with it the tension and its resolution. So I guess that's why you feel it sounds nicer when played together.
You could play this with just one guitar, BTW; just play the second part on the first and second strings and you'll get the same effect.