First off...when I train deadlift, I use straps for anything over 405...mixed grip up to that point. Deadlift and heavy bent over DB rows is all I use straps for. In my last strongman competition I was over/under handing my last deadlift, and sure enough popped my biceps tendon (distel). My grip was plenty strong...it was the biceps that gave out.
So, my advice is if you plan on competing, train the over/under grip all the time. If you don't...use straps. I think its just an overall safer option. There are other ways to train grip (FARMERS WALK!).