I’ve got a 2011 N14 JCW with a burnt valve (unconfirmed). Is there a difference between JCW and S heads? If so, is it significant?

 

Run your VIN in RealOEM.com. Look at the parts for JCW vs. S

 

Having a head treated by a machine shop (cleaned, new exhaust valves, change valve stem seals, new valve guides, redone seats) is probably the same cost as a used N14 head and will be just like new.
I believe the only difference up there is the thickness of the head gasket.