The correct one to use depends on your case. Those cables are typically used to connect front panel headphone/microphone ports. While the connectors may look identical, the pinouts are different and not really interchangeable. The matching connector on your case should be labelled accordingly, I know mine is labelled HD Audio.
HD Audio is intended to replace AC'97. HD Audio is generally more capable. The linked articles have more detail on that. For average home use, there shouldn't really be a noticeable difference.
The rest of this answer will be referencing the Intel Front Panel I/O Connectivity Design Guide, page 19. They also have schemantics on pages 20 and 25 if you care. I will be adding emphasis.
Front panel audio design in conjunction with motherboard audio header design is dependant upon the type of audio CODEC being used on the motherboard. In the past, AC’97 Integrated Audio CODECs were prevalent. With the introduction of Intel High Definition Audio, many new
motherboard designs are switching over to High Definition (HD) audio CODECs. Designers
should note that AC’97 and Intel High Definition Audio front panel motherboards and I/O cards implementations are different and may not be directly compatible or interchangeable
Some sources indicate that it is/may be necessary to switch audio output modes in the BIOS configuration or with a jumper. It is recommended that you look at your motherboard manual. My own motherboard (MSI P67A-C45) manual just says it's compliant with the Intel Front Panel I/O Connectivity Design Guide, not all that much information. Dell manuals describe it as
front audio (F_AUDIO) and don't indicate any such jumper, and only describe the BIOS option
Onboard Audio Controller as
Enabled or Disabled (Enabled by default).
Passive AC’97 analog front panel dongles (ones which leave the 5V Analog pin-7 line unconnected on the dongle) may be used with the Intel® HD Audio analog front panel header. But note that the front panel jack detection and re-tasking functionality will be lost as the AC’97 jacks cannot support connection to the SENSE line. In addition, software must be aware that an AC’97 dongle is being used with an Intel® HD Audio analog header since the software might need to dedicate codec ports that are connected to the header to meet the product’s intended functionality.