While warfarin (Coumadin) is the traditional well established anticoagulant, four new pills are currently available: apixaban (Eliquis), dabigatran (Pradaxa), Edoxaban (Savaysa), Rivaroxaban (Xarelto). Studies show that the latest drugs work as well as warfarin, however, we do not have enough data to rank these new pills from one to four.
No matter which one you use, there will be still a risk of bleeding problems, but lower if compared to warfarin. They do have some conveniences over warfarin mainly the lack of frequent blood tests (INR) and dose readjusting. They also do not interfere with vitamin K so there are no dietary restrictions and they do not have as many drug interactions. Apart from being a well studied and established, Coumadin has one more advantage. If you get a dangerous bleeding problem, there is an established "antidote" that can reverse its blood thinning properties and control the bleeding. For the new blood thinners antidotes have been recently developed and their efficiency remains to be proven.
These new additions to the blood thinner family may have some benefits, but that doesn't mean you should drop your Coumadin prescription. If Coumadin has been working fine for you, without bleeding problems there is no compelling reason to switch. Warfarin is otherwise safer for patients with kidney failure or with a mechanical heart valve.