Personally, I don't differentiate. Either seems acceptable usage to me.
New words, one handy idiom, and a 2-minute quiz — delivered to your inbox to keep your streak alive.
Ms Google says:
55,200,000 English pages for "suffer from"
1,830,000 English pages for "https://www.answers.com/suffer&r=67 with"
143,000 English pages for " of