With the higher protein content comes a higher quality protein. The higher quality protein is going to have a higher lysine value. Lysine is the first limiting amino acid necessary for growth. Without enough lysine in the diet (it cannot be synthesized in the body) a young horse will either stop growing or grow at a very slow rate. The higher protein feeds are formulated for growth so they will also have added lysine.
As far as the rest of the diet, yearlings have a rather small eating capacity so what they do eat needs to count. What type of hay, what's the quality and how much (in #s) are they eating? From the picture, the colt looks like he's got a bit of a hay belly. That would indicate that the hay is too high in fiber for his immature digestive system to digest properly. Getting them out on green grass is the best thing for them and you will probably find that that is all they need forage wise. I wouldn't offer BP or oil to a growing horse. I want everything they put in their mouths to be chocked full of nutrients that will contribute to their growth. BP offers nothing more nutritionally than average grass hay at a premium cost. Oil is 100% fat. No vitamins, no minerals, no protein, no carbs. Just fat. Adding a little alfalfa hay is good as it's high in protein, Ca and Vit A. If alfalfa hay is too hard to come by, add a few #s of pellets. As tempting as it is, don't throw a bunch of feed at him all at once. You would prefer for him to grow and catch up at a nice slow consistant rate.