1) "Violent emotions washed over me, and I was quite overcome." - I could not deal with the violent emotions that I suddenly felt.
2) "I just let the emotion wash over me, and concentrated on my task."
In 1), I felt the emotions strongly, and was upset.
In 2), I felt the emotions strongly, but I was able to deal with them. The difference is the verb 'let', which carries the connotation of 'ability to deal with'.