Both are defined as "making you feel strong feelings of sadness".
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Have a look at the alternate definitions of the words. Even when the use case isn't appropriate, they often colour the meaning of the one your looking at.
I would say that "moving" has no implication that the feelings are sad. Unless there has been further context given to imply such emotions, I wouldn't assume it. 'Moving' often evokes a response, e.g. being moved to action. Something 'poignant'; however, may be of intellectual interest in and of itself but not evoke emotions or action.
I see 'moving' as generally positive. If I find a piece of music moving then it may be uplifting. Strong sadness is possible, but only one possible emotion.