Patients taking warfarin have a nearly 50% lower risk for stroke than those taking aspirin, but their risk for major bleeding was twice as high. They noted that taking warfarin for four years or more may be more effective at preventing stroke and death. The key decision will be whether to accept the increased risk of stroke with aspirin or the increased risk of primarily gastrointestinal hemorrhage [stomach bleeding] with warfarin.
http://www.drugs.com/news/aspirin-effective-warfarin-heart-failure-study-37968.html