Do you care about playing your sport? Do you actually like Williams or Hamilton more or are you twisted up with Williams because it’s been the “best” for so long?
If you want to play. Apply to Hamilton. If you LOVE Williams because you’ve been going to homecoming since you were 2 apply to Williams.
Please don’t try to make a choice on the name brand of either school. Both are prestigious enough that you won’t have any issue getting your first job.