Never use a bad power supply. Here is a list of good ones.
http://www.tomshardware.com/forum/id-2547993/psu-tier-list.html
Points in favor of your Power supply:
1. ASUS may have shipped it as the power supply in one of their desktop pcs.
Points against your power supply:
1. Very old design with high 3.3V and 5V output and only 216W of 12V. 12V is used by Video and CPU today. 216w of 12V is much less that the label 350W output. (output figures from the sticker on the PSU as seen in the photo at Amazon.)
2. Price on EBAY is $20-$25. Not very many good $20 PSUs out there.
Net, I'd drop $40-80 on a good PSU.
Now for your actual question:
Definitely use the adapter if the power supply is any good. For example, an OEM power supply from HP or Dell or Lenovo.
Modular power supplies get a lot of love for their cable management. No one says anything about the extra connection needed because the modular cables are not soldered to the output inside the power supply.
Adapters add an extra connection. That is not something horrible. When using adapters make sure that you don't pull too many amps through the pins. For example an adapter that converts a 6-pin to an 8-pin is pulling too many amps through the original 6 pins (or they would have used a 6-pin instead of the 8-pin). Your two X molex to 6 pin PCIe doesn't have this problem. It uses the two 4 pins molex instead of only one molex to avoid pulling too much 12v through the pins. It's perfect.