Olympicnut,

As you said, you won't have much time in Christchurch. The TranzAlpine is a good ride, and it's well worth it. However, you can't compare that with driving it. Firstly, you can't see very much when you need to focus on the road...! The train tracks aren't parallel to the roads, so the train offered a lot more.

If you've more time, the TranzAlpine is a must.

Other things I'd consider given you time frame will be to get a car and head to Lyttelton and/or Akaroa/Banks Peninsula. Hanmer Springs will be good too, but again, that's a day trip...