My initial thought is that these two lines of thought are so disparate in history that it's hard to compare them. Hume is something of an deacon of the enlightenment (quiet follower who took many enlightenment principles to their rational end), and stoicism is an ancient doctrine we've gleaned through fragments that happen to be left over, and influenced by the ancient Greek milieu concern with invulnerability. Even the words like "control" and "passions" seem to differ to me, because the philosophy of mind and ethics of their day differed.

It's just hard to compare such notions in situ -- now, in vitro, with more explicit explanations of what you are thinking -- that's possible.

My initial thought is that these two lines of thought are so disparate in history that it's hard to compare them. Hume is something of an deacon of the enlightenment (quiet follower who took many enlightenment principles to their rational end), and stoicism is an ancient doctrine we've gleaned through fragments that happen to be left over, and influenced by the ancient Greek milieu concern with invulnerability. Even the words like "control" and "passions" seem to differ to me, because the philosophy of mind and ethics of their day differed. — Moliere

Well, yes, they are different philosophies of the mind; but, that doesn't negative they're importance at least.

The Stoic says that wisdom is to know that you cannot stop the rain, but you can fix the roof.
Hume says that you have a passion to stay dry, and reason is the slave that will help you satisfy your passion.

There seems to be no incompatibility.