You almost certainly have some Apple Scab. In addition some of the browning could just be transplant shock. Different varieties and possibly health differences of the two at planting are most likely why one was more affected then the other. It was a rotten year for apple diseases, both Scab and Cedar Apple rust are rampant because of all the rain. You do know that newly planted trees should not receive any fertilizer for at least one full growing cycle and better yet two full years. Neither of these problems will kill your trees.
How about getting rid of that grass up to the trunk and giving them a nice, shallow, mulch ring. Apples (I am told) are the worlds second most sprayed crop, here in the NE they get at least fungicide at bud break and then twice more. Many Apple farmers treat several more times if the weather dictates. Of course you can still eat the fruit scab worms and all, so will have to decide just how nice you will want your apples to be, then decide on a treatment. But you are still a few years from fruit.
If you plan to go organic then look into something called kaolin clay spray, for insect and disease control, looks terrible but is quite effective.
My best suggestion for you is to bring some samples to the extension service and pick up a few pamphlets on growing Apples while you are there.

Thanks.
I didn't fertilize any when I planted and I'll wait until after next year.
The grass is actually just a layer of clippings. I've got a couple inches or so of mulch around the tree but I had just mowed.
There weren't any leaves when I planted them. Would that still be transplant shock?
I'm not inclined to treat if it's not likely to come back next year. I'll get rid of the leaves when they fall.

Certainly can be, transplant shock does not only occur when leaves are present at planting. Sounds like you are doing right. In a year like we had it was not good for root growth. I know that sounds backward because of all the rain, but when it rains as much as it did this year in the spring and early summer, the ground does not dry out and starves the roots of oxygen that they and the tree needs to grow. I hope you planted at the right depth and all. Let them be now and as you say rake up the leaves.