Pretty expensive proposition either way. The concrete underpinning is obviously physically more disruptive.
Some people reckon run a hose where the house is sinking to re-expand the clay, or just wait for the wetter months and re-assess before committing to underpinning. If you have external cracks in your brickwork they could also in theory move as the soil moistens. Measure them now at a marked point and do so every so often as the weather gets wetter to see whether the extent that the problem corrects itself.
But often the problem lies deeper in the soil. This being the case, the above may be futile.
