Then what's the benefit? Why write a new bill that simply reiterated a previous one?
That was only a single provision in the bill. The entire bill does a lot fo things.
From wiki:
The Act authorizes $662 billion [4] in funding, among other things "for the defense of the United States and its interests abroad." In a signing statement, President Obama described the Act as addressing national security programs, Department of Defense health care costs, counter-terrorism within the U.S. and abroad, and military modernization.[5][6] The Act also imposes new economic sanctions against Iran (section 1045), commissions reviews of the military capabilities of countries such as Iran, China, and Russia,[7] and refocuses the strategic goals of NATO towards energy security.[8]
The most controversial provisions to receive wide attention are contained in Title X, Subtitle D, entitled "Counter-Terrorism." In particular, sub-sections 1021 and 1022, which deal with detention of persons the government suspects of involvement in terrorism, have generated controversy as to their legal meaning and their potential implications for abuse of Presidential authority. Although the White House[9] and Senate sponsors[10] maintain that the Authorization for Use of Military Force (AUMF) already grants presidential authority for indefinite detention, the Act states that Congress "affirms" this authority and makes specific provisions as to the exercise of that authority.[11][12] The detention provisions of the Act have received critical attention by, among others, the American Civil Liberties Union (ACLU) and some media sources which are concerned about the scope of the President's authority, including contentions that those whom they claim may be held indefinitely could include U.S. citizens arrested on American soil, including arrests by members of the Armed Forces.[13][14][15][16][17]