how people in England are taught about and view the legacy of the English Civil War.

There's a fair amount of scope in the curriculum but study of the civil war is not compulsory. The requirement for GCSE history (exam taken at age 16, history is not compulsory) is that a period of English history from 1450-1750 is studied, and schools will often choose the Tudor period, I suspect as people tend to have better existing knowledge and interest. It is more common for it to be studied at A-level (exam taken at 18, again not compulsory) and at least a couple of syllabus include it as compulsory.

So as for the legacy; I think the man on the street wouldn't be able to say much about it. They know who Cromwell is, and that the king was beheaded but not much more than that. It's less recent and casts less of a shadow over the current social climate (racism in America is seen to go back to slavery, whereas there's no hangover of Royalist/Parliamentarian sympathy)

Is one side lauded and the other damned?

Actual study does not tend to favour one side over the other, particularly. It does look at things like the intransigence of King Charles, but I wouldn't compare it to the American Civil War. In terms of my hypothetical man on the street; I think there's a common feeling that Cromwell was a tyrant. I'm quite interested in the Civil War and that's often the reaction I get back.