How timely. There is a very good reason it will sound like I'm speaking out of school here but I have not noticed one style to be any tougher on the biceps than any other. Then again bicep injuries are common in strongman..Many events are really focused on arm strength and that's what sets you up I think in a way that the occasional use of tire for conditioning might not.
With larger/thicker tires, 700-1000 pounds, many people cannot physically reach for an outside grip without narrowing stance so much that the tire is unstable once up or you unevenly overload the low back more than is ideal.
However..I think it's best to shift around and find what works well for you and allows you to use full body and hip drive to drive it up explosively.