It's a trade: a smaller power supply, or more video memory. ASUS recommends a 550W PSU for the ASUS Dual GeForce RTX 5060 White OC Edition 8GB GDDR7 and 750W for the ASUS PRIME GeForce RTX 4070 SUPER 12GB GDDR6X OC Edition, while the RTX 4070 SUPER carries 12GB of VRAM to the GeForce RTX 5060's 8GB. If you'd rather keep a smaller PSU, the GeForce RTX 5060 comes out ahead; if VRAM matters more, the RTX 4070 SUPER does.
Condition:
  • The 550W and 750W figures are ASUS's recommended PSU ratings for these two specific cards. They're recommendations, not stated minimums.
  • The GeForce RTX 5060 card takes one 8-pin power connector. The RTX 4070 SUPER card takes one 16-pin connector. Those are different connectors, so "one each" doesn't make them equivalent. Check which cable your PSU actually has.
  • ASUS lists both cards as 2.5-slot. That's a match on slot thickness only. It says nothing about length or whether either one fits your case.

The two cards, side by side

The two cards, side by side
SpecGeForce RTX 5060RTX 4070 SUPER
Power connector Not comparable1× PCIe 8-pin 1× 16-pin (12VHPWR)
Recommended PSU 550 W Wins750 W
Slot width 2.5 slots 2.5 slots
VRAM 8 GB 12 GB Wins

The catch

The RTX 4070 SUPER gets you 12GB of VRAM instead of 8GB, but ASUS recommends a 750W PSU for it, where the RTX 5060 calls for 550W.

Exact source claims

  • The GeForce RTX 5060 takes a single 8-pin power connector.
    Original quote
    Power Connectors 1 x 8-pin
  • The GeForce RTX 5060 lists a 550W recommended power supply.
    Original quote
    Recommended PSU 550W
  • The GeForce RTX 5060 is a 2.5-slot card.
    Original quote
    Slot 2.5 Slot
  • The GeForce RTX 5060 has 8GB of video memory.
    Original quote
    Video Memory 8GB GDDR7
  • The RTX 4070 SUPER takes a single 16-pin power connector.
    Original quote
    Power Connectors 1 x 16-pin
  • The RTX 4070 SUPER lists a 750W recommended power supply.
    Original quote
    Recommended PSU 750W
  • The RTX 4070 SUPER is a 2.5-slot card.
    Original quote
    Slot 2.5 Slot
  • The RTX 4070 SUPER has 12GB of video memory.
    Original quote
    Video Memory 12GB GDDR6X

Official sources