Sean Roberts posts on the Russian Rosary, which comes in older and a newer forms.
St. Seraphim (Zvezdinsky), the Russian Orthodox Bishop of Dimitrov killed in 1937 by the Soviets, composed a "Rule of the Mother of God" that is extremely similar to the Dominican Rosary.
The differences in the mysteries are noteworthy. The fifteen mysteries of St. Seraphim's Rule include the following: the Nativity of the Mother of God; the Presentation of the Mother of God; the Flight into Egypt; and the Miracle at Cana. The four mysteries of the (15-decade) Dominican Rosary that aren't present are the first four sorrowful mysteries. (The Crucificion is present in both, but the Russian decade is explicitly "in honour of [Jesus'] Mother's standing at the foot of [His] Cross.")
Overall, then, the Orthodox prayer emphasizes Mary's role in salvation, and the Catholic prayer emphasizes Jesus' passion. Typical choices, I think.