What goes better with tilapia and mashed potatoes

I'd vote for the green beans, for color contrast as well as to avoid adding a second starchy component to the plate. Your fish and mashed potatos are going to be looking pretty pale on the plate, and black eyed peas are not going to look really great against that. Though you could always make a black eyed pea salad- which would bring acidity and brightness to the plate.

Would you be using homemade black-eyed peas (i.e., cooked from the dried legumes) or from a can? Black-eyed peas can be a bit of an acquired taste if you're not used to them; if not, then green beans would be a safer bet.

Both would be good.
Depends on what you want more in this particular meal.
If added protein, the black eyed peas.
If the earthiness, minerals and vitamins of a vegetable, the green beans.