There is no advantage to choosing one over the other.
"Real" B+-tree implementations will often rebalance if they can, rather than splitting. When a node becomes overfull, if there is a sibling (whether to the left or the right) which isn't yet full, it's often better to balance the entries evenly between this node and its sibling. This saves an allocation.
My question was answered by email after I posted it here.
The answer is that the priorities of the elements can't be chosen completely randomly when an element is inserted into the treap that represents the set. The priorities need to be given by a hash function. That way, the same elements are always associated with the same priorities and the union ...