Also, if I were to buy a set of these 3rd party cables for my PS2, would they work with my Xbox also?
Some do, if they have the XBOX connector. In general though, I have found that 3rd party connectors have really poor quality parts and are not as good as 1st party parts. There are exceptions with companies like Monster, but those are rare. Basically, if you are paying a lot less for a part than the 1st party is selling it, expect lower quality.