Thanks for mentioning proof, good point. My earlier comments were based on the assumption of comparing bourbons of the same proof. But indeed when you dilute a whiskey, the whiskey will be lighter than at higher proof. A good example is that I have read when Jack Daniels was reduced for U.S. (domestic) sale to 80 proof, some older whiskey was put in the batches to match the color to that of the displaced 86 proof JD.
Jim Beam white label is 4 years old, so being a relatively young bourbon, and 80 proof, its color will be on the lighter side. Age statements of course do not mean the whiskey in the bottle or some of it isn't older: sometimes it is, and in the past, when there was more aged whiskey in company inventories than today, it was more common to encounter this. But it is probably safe to assume that that Beam white is not much older than 4 years. The Ezra Brooks has no age statement I believe, so it would be four years at a minimum but may be older or have some older whiskey in it, plus the higher proof should make it darker somewhat anyway all things being equal.
It's also true though the characteristics of each warehouses or parts of one are different, usually, so you will get different colors probably in different locations of each one and in one as compared to another. Each barrel differs too to a degree in color...
It's interesting to compare colors of numerous standard bourbons, they vary slightly usually - or at least by my eye - from batch to batch although the differences may be very small. Some brands seem good at maintaining color, especially Beam.
So there are many variables but I still feel that all things being equal, with a darker whiskey you are getting usually an older one and so the taste is more intense. Of course, intensity will not matter, indeed it can be a detriment, if the flavor - the profile of the brand - doesn't appeal.