Actually, you're posing two different questions, the difference between the performance characteristics of a hard wheat flour and a soft wheat flour as well as the difference in performance due to protein content.
Hard wheat flour v/s soft wheat flour: I lot of the performance characteristics will depend upon the varieties of wheat making up the grist that is being milled but in general, the gluten structure obtained with a hard wheat flour will be stronger than that from a soft wheat flour, think softer, more extensible doughs with soft wheat flour. Additionally, soft wheat flour typically do not have the fermentation tolerance exhibited by hard wheat flours to they tend to show more of the effects of fermentation, especially when longer fermentation times are employed. Some of the "00" flours reflect this difference by stating that specific "00" flour types are designed for long or short fermentation doughs, and they are correct, if you give a short fermentation designated flour a long fermentation time the dough can get pretty soft and extensible, probably more than what many people would care to work with.
As to the difference in protein content, in this case you have to compare the protein content only from hard wheat varieties, work that I did back in the 80's clearly showed that doughs were equally as strong when made using flours of the same protein content whether the flour was milled from a hard red spring wheat grist or a hard red winter wheat grist. We found this to be true over a wide range of protein levels. In our view at the time these results totally debunked the premiums paid on spring wheat over winter wheat at the time, kinda irritated the branch of the U.S. Government responsible for the export of U.S. wheat at the time.
Tom Lehmann/The Dough Doctor