This is a complex question, and regardless of what is said here, the best option is to discuss this with your father's physician to make the final decision based on his full medical history and current health state.
Coumadin (warfarin) is among the oldest of anticoagulants. It is broadly approved for many uses, including treatment of DVT and of atrial fibrillation. The difficulties with warfarin are much as you stated (dietary restrictions limiting Vitamin K intake, frequent monitoring required, and possibly frequent dosage adjustments). The advantages are that it is incredibly cheap (dollars a month, rather than $5-10/day for newer drugs), and reversible relatively quickly if necessary (with fresh frozen plasma infusion or Vitamin K administration).
Pradaxa (dabigatran) is a new drug which is approved for treatment of patient with afib that is not due to valve abnormalities. There is evidence from studies that in patients over the age of 75, there is increased risk of extracranial bleeding (outside the head) compared to treatment with warfarin. Advantages include no need for routine monitoring, and standard dosing. However, disadvantages include difficulty with reversal if bleeding occurs, and cost.
Xarelto (rivaroxaban) is a newer drug which is approved for afib not due to valve abnormalities (like Pradaxa), and prevention of DVT after orthopedic surgery. Advantages again are easy dosing and no need for monitoring. However, disadvantages are extreme price, difficult and unproven to reverse.
In your father's situation, he technically could be treated with any of the three. However, you state he had multiple falls in the past year. With any of these meds, that is a risk that he could bleed catastrophically if he were to injure his head, though reversal with warfarin would be fastest of them. If he was falling frequently, sometimes the risk of staying on these meds (bleeding with fall that could lead to death) outweighs the benefit (stroke prevention which is a few percent per year), which is something his physician needs to determine. Given his age, and history of blood in stool and falls, it is reasonable to keep him on warfarin (coumadin), especially due to the evidence in people over 75 on Pradaxa, and the difficulty of reversal with Xarelto given his falls history. However, all of this should be discussed with his physician, and final decision will depend on many factors which go beyond the scope of this forum, including his physical exam and current health status.
Thank you for your comment; i know that plavix was not designed for Afib, but could that be used for stroke prevention instead of coumadin when the individual can not tolerate coumadin and longer? we are searching for anything that could provide a better quality of life for him and since the coumadin is clearly effecting his memory he has said that he's about done with it and wants to just get off of it. I know that this could be dangerous for him, so we're trying to find something that would afford him some protection from a stroke before he refuses to continue to take the coumadin. Could Plavix and asprin be used together to help with stroke prevention or is Plavix just as dangerous and Xeralto and Pradaxa? Thanks