It is certainly better to use the word productive than busy. The productive one generates something and the busy one does not necessarily.
It is better to refer to the first word, the brain will take it better and the person will be much less overwhelmed. The busy one cannot always solve the productive one can.
I feel more productive than busy, although sometimes it happens to me that I am very busy with many things, not only work, but the focus is what helps me in those circumstances.
Focus is important. We all have many things pulling and pushing us in many directions and it's easy to succumb to it but if something is so important then it's worth devoting full focus to it right?
Yes it's true... focus, prioritise and move on!