It depends on the particular Church sui iuris and may even vary from parish to parish. I’ve known plenty of Eastern Catholics who wear the brown scapular, pray the rosary daily, and could tell you more about Roman saints than they could about Eastern saints. I’ve also known Eastern Catholics who all but despise Roman devotions and, while they’re aware of Western saints, would prefer not to talk about them. But in my experience the bulk of Eastern Catholics are somewhere in the middle between those two extremes.