According to Katzner's dictionary, сложно is an adverb only and means "in a complicated way", while трудно is either an adverb or a predicate adjective (pred.adj. are separated by a verb from the subject, e.g., "It is difficult") which means "with difficulty" or "difficult". Complexity doesn't necessarily mean difficulty - some complex tasks are simply tedious, not difficult if you follow the steps.
The English translation is ok, but a bit liberal, and makes you think that dative in моим словам depends on трудно (a predicate I ignored so far), like, say, "мне надо". The literal translation "It's hard to believe my words" clearly suggests that "моим словам" is the object of верить, which, as we have learnt, wants dative.