Use a photo of you for your personal profile on Facebook and an image of your art for your business page.
Yes, it's nice to see artists' faces (I agree! I like to see faces, too), but are you promoting your face or your art?
When people visit your art page, you want them to be wowed immediately. You want your page to scream, “I'm an artist! And I'm a damn good artist!”
As pretty or handsome as you might be, your art should be the star here.
The #1 Reason
The main reason you use your art as your image on your business page is this:
When you comment on other pages as your page, you leave an image of your art on those pages. If someone likes it, they might click on it.
I know of at least one artist who commented as her page on my Facebook page and was then asked to show her art at a gallery. The gallery saw the image next to her comment and contacted her.
This wouldn't have happened if she had left a picture of herself next to her comment.
To confirm: face on personal profile and art on business page.