IIRC, I think Cliff said somewhere that the needle tuner uses a pitch average of the whole signal, while the strobe tuner uses only the fundamental of the note. If the upper harmonics of the string are skewed one way or the other compared to the fundamental, you can get different results between the two tuners. If you turn your tone control all the way down on your guitar, you'll probably see less of a difference between them since that rolls off much of the upper harmonics and leaves you with closer to a sine wave.
I read somewhere many moons ago to not use harmonics to tune or intonate, but rather use open strings and fretted 12th since the harmonics can sometimes be a bit off depending on how you hit them and the particular strings on the guitar. No guitar will ever intonate perfectly, so it's always been one of those "close enough for rock and roll" things for me. Hell die hard Tele snobs claim that the vintage 3 saddle design's inability to intonate well is a key part of the Tele's character. I'll take a more modern compensated version any day personally.