It comes down to two numbers. ASUS recommends a 550W PSU for the RX 9060 XT and a 750W unit for the RTX 4070 SUPER. The RTX 4070 SUPER has 12GB of VRAM, while the RX 9060 XT has 8GB. So if you want a lower PSU recommendation, look at the RX 9060 XT; if you care more about memory, look at the RTX 4070 SUPER. Both cards are listed as 2.5-slot. They each use one power connector, but it's a different type on each card, so the connector doesn't make either one better.
Condition:
  • The 750W figure is ASUS's recommended PSU for the PRIME GeForce RTX 4070 SUPER 12GB GDDR6X OC Edition, not for every RTX 4070 SUPER card.
  • The 550W figure is ASUS's recommended PSU for the Dual Radeon RX9060XT 8G GDDR6, not for every RX 9060 XT card.
  • The RTX 4070 SUPER's 12GB is GDDR6X. The RX 9060 XT's 8GB is GDDR6.
  • The RTX 4070 SUPER takes one 16-pin connector. The RX 9060 XT takes one 8-pin connector.

RTX 4070 SUPER vs RX 9060 XT: the spec sheet

RTX 4070 SUPER vs RX 9060 XT: the spec sheet
SpecRTX 4070 SUPERRX 9060 XT
Power connectors Different types1× 16-pin 1× PCIe 8-pin
Recommended PSU 750 W 550 W Better
Slot width 2.5 slots 2.5 slots
VRAM 12 GB Better8 GB

The easy-to-miss part

ASUS recommends a 550W PSU for the RX 9060 XT and 750W for the RTX 4070 SUPER. But the RTX 4070 SUPER has 12GB of VRAM, while the RX 9060 XT has 8GB.

Exact source claims

  • One 16-pin power connector
    Original quote
    Power Connectors 1 x 16-pin
  • Recommended PSU: 750W
    Original quote
    Recommended PSU 750W
  • 2.5-slot card
    Original quote
    Slot 2.5 Slot
  • 12GB of GDDR6X
    Original quote
    Video Memory 12GB GDDR6X
  • One 8-pin power connector
    Original quote
    Power Connectors 1 x 8-pin
  • Recommended PSU: 550W
    Original quote
    Recommended PSU 550W
  • 2.5-slot card
    Original quote
    Slot 2.5 Slot
  • 8GB of GDDR6
    Original quote
    Video Memory 8GB GDDR6

Official sources