Broad, wide, deep are comparable chiefly when they refer to horizontal extent.
Broad and wide apply to surfaces or areas as measured from side to side and deep (see also DEEP) to those as measured from front to back.
Broad and wide always and deep in some instances may be used of surfaces that spread away from one; thus, a river may be wide or broad (but not deep, which would here refer only to vertical distance) at a given point, but a flower border may be four feet wide, broad, or, if the far side is not ordinarily accessible, deep.
When a plot of ground or similar area is measured, broad or, especially, wide is used of the distance from one side to the other and deep of that from front line to back line.
Broad and wide are frequently interchangeable when used descriptively to mean having relatively great extent across or from side to side.
But broad commonly applies only to surfaces or areas as such.
Wide applies also to apertures or to something that opens or spreads. Wide, therefore, is the preferred term when the emphasis is upon the distance between limits rather than on the extent of the intervening surface.
Deep in similar descriptive use, when it carries an implication only of horizontal extent, is applicable only to something that has great extent backward (as from an opening or from the front).