Addison Reed, the current closer for the Chicago White Sox, was drafted on the same day in 2010 as his brother, Austin. Austin, however, is a pitcher in the Cubs organization. They are looking forward to the day when they will be facing each other in a major league game.
My book, Family Ties: A Comprehensive Collection of Facts and Trivia About Baseball’s Relatives, has a chapter on brothers as teammates and opponents, with a lot of fascinating anecdotes.
See attached article on whitesox.com about the Reeds.