Livers seems to be head and shoulders above Race as far as handles is concerned (I've never watched a full game of Livers).
Here's a link to Race's stats from the season. http://www.mnbasketballhub.com/roster_players/15609457
Head coach neglected to put a lot of his FGA, 3FGA, and FTA on there. Mostly because of scouting reports that burned him in the past (my team fouled the crap out of one of his former players because that coach posted all of his FT shooting).
I just don't see Race being a fit within Beilein's system. I think he is a talented player but more of a traditional 4 than a normal 4 that Beilein has had. He doesn't do enough not the perimeter (ball handling and shooting) to make it work. I believe (no inside info) he really wants to be a "stretch 4" but isn't there yet.