You could check out the very interesting and thorough research over the last 10 years on braided channel dimensions, evolution and dynamics in some of the world's largest rivers (e.g. South Saskatchewan River, Canada; the Parana etc.) by Gregory H. Sambrook Smith, Philip J. Ashworth, Jim Best and Stuart N. Lane. You could search on Google Scholar, for example. That body of work would give you a good start in establishing the evidence base to test out answers to your question on width and depth of braid channels. They often use GIS, digital elevation models and ground-penetrating radar approaches.

For example, see this recent paper below on the South Saskatchewan River, Canada - and its large reference list too:

"Quantification of the relation between surface morphodynamics and subsurface sedimentological product in sandy braided rivers"

by

Natalie O. Parker1,

Gregory H. Sambrook Smith1,

Philip J. Ashworth2,

James L. Best3,

Stuart N. Lane4,

Ian A. Lunt5,

Christopher J. Simpson6,

Roberte. Thomas7

published in Sedimentology, Volume 60, Issue 3, pages 820–839, April 2013

Hope this helps to get you started!