This fancy word for "busy" makes you sound much more organized. "Busy" sounds like you're overrun, with papers and calendars flying around, hardly enough time to brush your hair in the morning, and overall pretty sloppy. "Assiduous," on the other hand, makes you out to be devoted. You have so many things to do because you're caring enough to take them all on, then complete them all. Only problem is, you'll sound a little funny saying calling yourself "quite assiduous lately" in casual conversation. It's true, though, that they're not exact synonyms. Busy is just defining the amount of work you have to do, while assiduous explains how you approach your work.
Me, I'd like to say I'm being assiduous. If I don't get done with the day's work until late, I still read a chapter or two in the book I'm reading right now (title to be disclosed once I finish it -- hopefully in the next week.) That means I've been getting to bed past eleven . . . hurray for Saturdays to sleep in. But in my present assiduousness I must be going now.