That was my first thought as well. As long is in tune and the intonation is set correctly, the two notes will be identical, but the note color (I believe it is called) will be different. The sixth string fifth fret A sounds more muted, softer than the same A on the fifth string open.
That's for two reasons: 1) the fifth string open is open, so it naturally sounds more vibrant, and; 2) as the strings get thinner they also sound more vibrant, or peppy, or whatever word you want to use for it.
That's why the F on the first string first fret sounds different than the same F on the second string sixth fret, while the same F on the third string tenth fret sounds different than both of those, and the same F on the fourth string fifteenth fret sounds different still.
Taking it to the max the same F note on the fifth string twentieth fret sounds still different. As you play those five identical pitches you will hear distinctly different coloring of the pitches even though they are all identical (if you're in tune and your intonation is correct).
This is incidentally why some guitarists sound different or better than those who learn to play their songs. The original guitarist sometimes chooses an "unusual" fingering for the notes, making them sound a particular way that he or she wanted them to sound, and people learning to mimic those notes often choose the easiest way to play them.
That fact hit me in the face when I watched Tony Iommi play Paranoid for the first time. Just about everyone learns to play that riff with a fifth string root. He plays it (or did some time ago) with a sixth string root so the guitar sounds more moody, more Black Sabbath.
That's also why you'll see pop guitarists playing only the top three strings. They sound brighter, so the guitar has a distinctly different sound.
Man, I could go on all night about this stuff. :D
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