Counting differences between dialects involves a lot of boring questions about which contractions, changes of pronounciation or grammar etc. count and which don't. Does "I'm like" in the sense "I say" count? There are too many low-value questions to really get neat precise numbers.
American English: "A source for that? I would be surprised it was actually 99%."
Maybe if you count spelling, it might be less, but it's not like 'colour' and 'color' are different words in functional terms.
But in common use I wouldn't be surprised if it was 98% or less
consider words like "pissed", "pants", "suspenders", "fag", "chips", "bisquit", "jelly", "pavement", etc.
they mean different things in British and American English, even though etymologically they come from the same source
I would. One bit of evidence against this is the amount of the Extra's script Ricky Gervais had to rerecord for an American audience. Most of the change was for unshared cultural references (local food brands etc.) and only a couple for words (fanny).
Due to the level of exposure, I believe the difference between generic Brit and generic US is less than the dialects within the countries e.g. older generations of Yorkshire vs. Cornish, Glaswegian vs. Cockney etc. can suffer great difficulties understanding each other.
The number of unshared words is much higher, methods of denotation and sentence construction are different and even the pronunciation of shared words become unrecognisable (I'm not a linguist, so open to correction). I'm sure there are similar extremes in the US.
They were complains of American fans not understanding Peter Capaldi as the new Doctor, as he has a (VERY understandable) Scottish accent.
Besides, nobody understands Southerners anyway.