Too narrow it down to just one single feud would be hard because there have been around six or seven great feuds since 2005 in WWE and three or four in TNA and i guess it would simply come down to personal opinion which everyone has a difference on. In WWE since 2005 i would say Cena/Edge, Michaels/Jericho, Michaels/Undertaker, Undertaker/Edge, Hardy/Punk, Triple H/Orton going into WrestleMania 25 and the first half of Cena/Nexus would all class as the best in WWE since 2005 and over in TNA i would say Joe/Angle, Styles/Angle, Styles/Daniels/Joe and the first half of The Frontline/Main Event Mafia.
If someone held a gun to my head and said pick one then because of how long it went on for and how WWE managed to elevate each man to a whole new level whilst also going through almost every match possible including my personal match of the year from that year i would go with Cena/Edge. In this current time in the industry to have a feud go from January through to October and for it to still draw people in is a complete rarity but WWE managed to do it, what WWE did well with Cena/Edge was throw other people into the mix like Triple H, Rob Van Dam, ECW, D-Generation X and Cade and Murdoch all at different times to keep it fresh and for their TLC match at Unforgiven was the best match that year.