Mopar
They all built some pretty hot cars in the 60's but it all depends on what "best" represents for each person. Styling, performance, reliability, price? If I were to choose who made the most powerful cars from 1960 -1969, Chrysler would probably be my choice. They were shoving big cube, dual quad, big HP motors in any family car you could choose well before the popularly known "muscle car" era started in the late 60's. (Ie: 1961 Chrysler 300G, 413 cu.in., 4 spd stick, 400 HP, ~500 ft/lb, with dual quads) Everyody knows the Wedge and Hemi motors (especially Hemi) for ruling both the drag and Nascar circuits back then. Not to say that all other brands didn't build some sick powerful cars as well like the 69 ZL1 Camaros, the Yenko's, the Shelby's, 428 CJ Stangs, Ram Air GTO's etc... but Mopar kicked a lot of GM, Ford and AMC ass with the Hemi then and still to this day.