You must use 42.3w Sq/Ft of the very best LED Diodes to equal a 1000w HID.
Gavita 1700e 645w is a direct replacement for a 1000w Hortilux HPS in a 4 x 4 area. No way around it, though it blows the budget out of the water.
Best budget LED are HLG, and will still be more than a $500 budget. They use Samsung/Osram Diodes. Dont use any other Diode if you want as good as results as HID. But you must use 42.3w Sq/ft regardless. 1000w HID/Hortilux is 1600umol, and 62.5w Sq/Ft.
Gavita 1700e is 645w, and 1700umol
Gonna take about $800usd-$1000usd for the HLG.