[Tim Farrant]

As David points out, the size depends on the type of metal used for the core. Older metals meant bigger transformers to acheive a similar output level before saturation compared to the modern core types in use today. Most transformers will saturate at low frequencies first, hence the "warmth" that is actually low freq harmonic distortion. But yes, generally speaking, a bigger trnaformer will handle more level before saturation.

Cheers
Tim.