Answer
Usually less, and often much less. This surprises buyers who assume a newer machine must be hungrier.
The entry class has fallen sharply across three generations. A Power 9 S914 is rated at 1,600 W, the Power 10 S1014 that replaces it at 1,075 W, and the Power 11 S1112 at 550 W. That is roughly a third of the load in two generations, and the S1112 will run on a standard 120 V circuit where the S914 usually did not.
The scale-out class is broadly flat. A Power 9 S924 and a Power 10 S1024 carry the same 2,750 W rating and the same 4U footprint, and the Power 11 S1124 is 2,950 W. The rating barely moves while the work done inside it rises considerably.
The multi-drawer legacy machines are where the saving is largest. A 32-core Power 6 Power 570 is four stacked drawers at 5,600 W across 16 rack units and roughly 254 kg. A Power 11 S1124 replaces it in 4U at 2,950 W, which removes twelve rack units, about 210 kg and roughly half the electrical load.
The exception is the midrange four-socket line, which has grown each generation: E950 at 4,220 W, E1050 at 4,950 W, E1150 at 5,400 W. If you are moving up into that class rather than across, plan for more capacity rather than less.