Looks like that answer was copied directly from this 2008 post on a different forum:
https://forum.wordreference.com/thre...-sense.953244/
That answer was provided by someone from the UK, so we Americans may have a different point of view. I agree with JoyP that there is little difference between the two phrases. But there may be nuances. I think "broadly speaking" is used to signal that the statement that follows is a generality that probably has exceptions. For example: "Broadly speaking it is warmer in Hawaii than in the Arctic." Generally this is true, but there are exceptions. (Side note - my brother was caught in a blizzard once while in Hawaii.) The phrase "in a broad sense" is used when you want to expand the definition of something, i.e. allow greater freedom of how something is defined, or draw an analogy. For example one might say "In a broad sense the Earth is a living organism." Now the Earth is definitely not a living organism, but this helps convey the fact that there are certain aspects of the Earth's ecology, geology. meteorology, etc that act in ways that are similar to how a living organism interacts with its environment. But you wouldn't say "Broadly speaking, the Earth is a living organism."