As I looked skyward, I wasn't considering if the branches were alternate or opposite, a common way to differentiate tree species, but rather how the branches in the crown looked. Were the branches straight or crooked? Were they fuzzy or more feathered looking, suggesting many small twigs rather than just a few as the branches came to an end? After doing some research on branch density, I discovered the term bifurcation ratio, which is the ratio of numbers of distal to proximal branches and is a quantity which can be used in conjunction with other parameters in order to understand branching strategies. Additional research determined that bifurcation ratios are indeed species specific with some exceptions.
It seems certain species, such as Acer, will have higher bifurcation ratios when grown in open areas with lots of light and less competition, compared to those found growing closer together in forests. Bifurcation ratios for Quercus and Fraxinus don't show variability when grown in different environments, for some reason still yet to be understood.
Of course I found all of this information fascinating and was amazed at what one can learn when a simple question is asked. Now I just need to put a face or name to each different branching pattern.