This would depend upon when this conversion took place. If Vladimir I of Kiev chose Catholicism over Orthodoxy, this would mean Byzantium would have a potentially dangerous rival to the North, rather than an religiously sympathetic one. A catholic Russia would be more likely to adopt the Latin script, rather that the more Orthodox oriented Cyrillic.
A Catholic Russia would put that country in the West's orbit from that moment forward. Though it would be a rather backward member of that club, it would still follow Western religious and intellectual trends, even if it lagged by a century or two. Russia would probably influence the West to at least some degree, as I imagine that Russian devotional art, especially iconography would become more acceptable in the West.
Religiously, I imagine that a Catholic Russia would be profoundly conservative, and highly resistant to "liberalizing" trends like the Protestant reformation. This would be due, in no small part to the immense distance separating Russia from the cultural centers of the West (Rome, Paris, Northern Italy). Also this could lead to a very different ideal of Russia, as it would be unlikely as the Tsars would see themselves as the heirs to the "Second Rome" after 1453.
The departures from OTL history are almost unlimited, and mostly, I think, would be positive in that it could lead to a more Western oriented Russia, one far less prone to conflict with the West.