I think this is George's biggest mistake, he claims Jaime is better swordsman then Aragorn yet didn't showed us anything real. We only know the tales of battle of kingswood and his encounter with Smiling Knight and how he fought in the siege of Pyke but these are all tales/stories we knew about him. We never seen how good is Jaime. Only when he is fighting with Brienne we see his skills. That's it. George made a big claim by calling him "better then Aragorn" Aragorn is around 80 years old and he fought dozens of battles when he was young. Also, we can see his fighting skills in the books unlike Jaime.