Both can be true. Standards can both have improved since the 1920s and income inequality can be equivalent or worse than the gilded age. This would be coherent with improvements mostly being funneled to the top, while some benefits accrue throughout the economy.

However the story is much more dynamic and interesting than that, with income inequality shrinking until the late 70s and early 80s, then expanding drastically until now, half a century later. That period of lower income inequality is mostly why things got better for the working class (but science and technology have marched on regardless).