These two men together revolutionized the theory and practice of medicine
I believe that in any situation where one can be used, the other would also be correct and would be understood to have exactly the same meaning.
However, they roll off the tongue differently. You might choose one or the other based on the way the resulting sentence sounds.
You both made it! That's great!
Both of you made it! That's great!
To me, the first example comes across as a quicker, snappier way of saying it. The way the sentence is stressed:
You BOTH MADE it.
The meaning is squeezed into a small four-syllable package that's quick to say.
The second one:
BOTH of you MADE it.
The sentence is perfectly alright, but to my ears, it lacks the same quick punch as the first example. It rolls.
It works the other way, too.
You're BOTH WELcome to COME.
BOTH of you are WELcome to COME.
In the first example, the two punches of stress in "BOTH WELcome" come together, book-ended by un-stressed syllables, with the COME hanging on the end.
The second example sounds more patterned. The "are" tends to join with the "you", with a resulting stress pattern like:
ONE two three ONE two three ONE.
I'd normally tend to choose the second one in this context, not because I'd stop and actually think about it before speaking, but because it sounds "rounder" to me somehow, and my mind would naturally "roll" that way.
But again, the