If the seat is a lot higher than the bars, then your torso could be too low which could cause neck pain from craning your neck up. Also, if the seat is too far forward, then you could have too much weight on your hands, and the constant pushing against the bars will cause neck pain. If your seat set back is correct, you should be able, while on the drops, to take both hands off the bars without the sensation that you are falling forward.
Also, it could be your riding style. Your arms and neck should be completely relaxed when you ride, so relaxed that if someone pushes your arm, it should just come off the bars with no drama whatsoever. If your shoulders are scrunched and your arms stiff, then try to relax.
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Il faut de l'audace, encore de l'audace, toujours de l'audace
1980 3Rensho-- 1975 Raleigh Sprite 3spd
1990s Raleigh M20 MTB--2007 Windsor Hour (track)
1988 Ducati 750 F1