Student or Learner
Is the brook larger than stream?
Think of them as being two words meaning the same thing.
Ask a geologist and he or she will tell you:
Stream - any body of moving water that moves under gravity to progressively lower levels, in a relatively narrow but clearly defined channel on the surface of the ground.
Brook - a small stream or rivulet, commonly swiftly flowing in rugged terrain, of lesser length and volume than a creek. A term used in England and New England for any tributary to a small river or to a larger stream.
But for us less technically-inclined folks, it is usually presumed that a "stream" has a strong current in a particular direction, while a "brook" is a smaller, narrower, "softer" version of a stream (if there is a current, it is not very strong, hence the term "babbling brook").
And what about "creek"?
Yes - 'creek' is common in AE, Dave, though much less so in BE.
With respect to Ouisch, I would still recommend to the OP that brook. stream, and creek are virtually synonymous for all practical purposes.
We do tend to use "creek" here. Weathermen often warn about flooding of "creeks and streams," but I never hear them say "brook."
"Brook" almost seems more like a poetic word.