Tires are commodities so make your decision mainly on price. As said above tirebuyer just the customer portal into American Tires.
It ends up being more about the shop you ship them too (unless you're really buying directly to you and you mount your own tires).
Differences in the shop choice will affect your experience more than choosing tirebuyer over tirerack over letting the shop order for you from their favorite distributer (which might be American Tire anyway).
Look out for coupons if you can find one.
I bought from them last year, nothing out of the ordinary, but after the order was submitted, I only interacted with my shop for everything, not tirebuyer.