Pulmonary Embolism Support Group
By far the most common form of pulmonary embolism is a thromboembolism, which occurs when a blood clot, generally a venous thrombus, becomes dislodged from its site of formation and embolizes to the arterial blood supply of one of the lungs. Symptoms may include difficulty breathing, pain during breathing, and more rarely circulatory instability and death.
Six months is the most common length of treatment, but people may stay on longer for a variety of reasons. Definitely question your docs further on their reasoning.
Ultimately, it will be up to you. No one will drive out to your house everyday to force the meds down your throat, so it is good if you do your research and ask questions and figure out what you, personally, are comfortable with.
I agree with RMB and TNT, talk with both doctors and ask to explain their reasoning and opinions.
With anything, it's always best to discuss any questions or concerns you may have with your Doctor. And worse case scenario, you can always try for a second opinion.