Both however, are less stressful to write than an academic paper

I have to disagree.
I've completed many copy writing assignments for business clients and it's just as stressful, if not more so. With an academic paper, you have references (and instructions) to back up your work.
In copywriting, you are at the mercy of your client's perception of what you've written. If Bob's in a bad mood today, he may find your writing less compelling that he did yesterday. Or perhaps Bob loves the piece but the rest of his team doesn't. Whatever the reason, you can be hit with several revision or even full rewrite requests.
Copywriting is similar to designing an ad concept... you don't know 100% that your work will hit the mark until the client sees it and, at the end of the day, their approval is the defining point of a successful project. In copywriting, like in graphic ad campaigns, the client generally has the final say on whether the project is accepted (paid) or rejected (not paid/refunded).
Of course, there are a few ways to avoid endless revisions/rewrites by making sure the client understands and agree to your policies before the project begins, but still, that doesn't mean the client will accept the project.