| You will need to be more specific. ie what partition do you require? A partition between a corridor/ kitchen for example is different to an acoustic partition?
Generally speaking, in the UK, steel partitions are cheaper. Steel however, has a lot of embodied energy compared to timber, so timber is the more sustainable option. what are the finishes to be applied to the partitions?
I also think steel partitions can be slimmer than timber partitions, although i may be wrong here. You can probably go down to 75mm thickness for steel partition, compared to 100mm thickness for timber.
Be more specific.
Also consider the feel for the space. Timber moves, whereas steel and concrete are very static. Walking across a timber floor is a different experience to walking across a steel/ or concrete floor.
What is the main frame for the house? Maybe you want to build a timber house? Then surely a timber partition would be the sensible option? Whereas a glass and steel house would suggest steel....etc | 
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