The bear skull on the right belonged to a 3 year old female black bear. The bear skull on the left was a quite old grizzly who died in a zoo. Here's the thing, and I cannot think of a better way to illustrate the point other than laying them out side by side: Give or take a million-or-so years ago - these bears were the same size. The Pleistocene was freakin' huge.
But neither of them could put a dent in a giant short faced bear. Not only was it twice the size of a brown bear, (Think of a grizzly or Kodiak bear and then double it,) It was also built for speed. You only had to worry about running into a giant short faced bear if you lived on the North American continent during the Pleistocene, but if you met, there is a high probability that running would definitely be involved.
Sticking with the Pleistocene theme, brown bears with us today first appeared in Asia and then spread to North America and Europe. Not without a sense of irony, they would have passed by the giant pandas who first appeared in Europe during the late Miocene and then made their way to eastern Asia during the Pleistocene.