There are a few differences between striped and black oil sunflower seeds. Most particularly, black oil sunflower seeds have thinner hulls and are easier for songbirds to open and eat. Black oil sunflower seeds also have a higher fat content. That said, when it comes to choosing which to offer your chickens, it probably won't matter very much.
Chickens don't open the seeds like songbirds do before eating them--they swallow the whole thing, hull and all. The seeds get ground up further down their digestive tracts, in their gizzards. So "easier to open" is just a moot issue with chickens. And as a treat offered in moderation, the difference in fat content between black oil and striped probably isn't going to make that much of a difference--sort of like choosing between snacking on cashews or pecans. They are both nutritious and high in fat, and while a few are good for you, eating too many will mean you're eating a LOT of calories.
So, as with any treat, offer sunflower seeds somewhat sparingly to your flock. Despite the fact that they are high in nutrition, they are not a complete, well-balanced feed, so make sure the majority of your birds' diet consists of layer pellet or crumble! And finally, make sure you're offering fresh seed. Sunflower seeds of both types have a high oil content (averaging near 30%), and can go bad if it sits around too long.