"Homework is hard."
Well, they're similar, but not to the extent I'd call them synonyms. In English, "hard" can be used to mean "difficult", but that too is contextual. E.g. if you're talking about something that is "not soft", you can't say it's difficult. The same goes for むずかしい and たいへん; they can have the same function, but aren't interchangeable.
Like you said, たいへん carries more judgement; a situation you find awful/severe, and clearly negative, while むずかしい is something complicated/serious, but a little more 'neutral'.