When? Where? And for whom? Depending on which civilization and which category of people, we will see different results. Also is a brogan a high shoe or a low boot? Questions of this nature are hard to distinguish without more precision.

There isn't really a transition from boots to shoes at any point in history. Boots (as we think of them) are incredibly complex to make since they require fitting the ankle, and sometimes the calf, as well as the foot. What you're probably seeing in medieval imagery up to the 17th century are hose that cover the whole leg, or sometimes even fabric wrapped leg covers. Most early shoes are very simple construction, utilizing the turn shoe method of sewing everything together inside out and flipping them. This means the leather has to be fairly lightweight in order to fold in on itself for turning. Heels came into fashion in the 16th century and that's when sturdier construction (and therefore boots) came in as well. Both shoes and boots use the same construction methods: welted, randed, or channel. The soles wouldn't be different weights for that reason, just based on the intended purpose of the footwear (dancing vs. walking). Boots originally were not meant for walking around. The leather was too heavy and stiff to be comfortable that way. Instead they were meant for riding or other protective activities. This changes in the later 18th century with the use of Russian leather (which no longer exists due to secret methods being forgotten). It was a much stretchier, lighter, but still strong, leather which allowed for nearly second skin fit that stretched easily and bounced back. This is when you can imagine the English gentleman in every Jane Austen book trouncing around his estate in knee-high boots. At no point, however, were boots more common than shoes for men. Boots were still complex to make and required a lot of leather, and therefore more expensive. Cheaper options for leg protection, such as spats, leg wraps, trousers, etc. were better choices for most.