It's not the director's cut, but it's a common misconception. There's a whole featurette about it on the DVD/BD, in which Park explains that he originally planned to do it so that he could be the first person to utilise the process, but changed his mind. It does slightly conflict with his comments in the introduction on the disc though.
The film has had numerous releases. The original Korean 2-disc SE had both the fading and colour versions, but - and it's a big but - the colour version was far more muted than the true theatrical version. It's like they changed the colour timing ready for the fading version and then just used that altered colour version on the second disc. The US and UK DVD were the theatrical versions with more vibrant colours. The UK got the fading version as part of the VT boxed set, but the theatrical version wasn't in that so you had to buy both. The Hong Kong DVD had the theatrical colour scheme as well.
I got the theatrical version from DDDHouse because they were the cheapest. Still cost me about £19.50 with shipping, which is the second highest price I've ever paid for a single BD. I'm a bit of a collector when it comes to the trilogy though, so I had to have both. So far I have:
Mr. Vengeance
Korean 2-disc SE
US single disc
UK BD
Oldboy
Korean SE
Korean FE
UK BD
Lady Vengeance
HK DVD
US DVD
HK BD
Also got the VT boxed set with the hammer etc. Always meant to pick up a cheap copy of the UK Oldboy on DVD for the extras, but never got around to it.
I know it's an Oldboy thread and I've already hijacked it a bit, but I thought I'd add a couple of caps to illustrate the Lady V differences for those interested. These are from a scene
before it starts to fade to black and white!
Even in this scene you can see how the detail is crushed by the colour changes.