Major differences I\'ve seen are:
#if, #unless, #with, and #each
One more subtle difference is the treatment of falsy values in {{#property}}...{{/property}} blocks. Most mustache implementations will just obey JS falsiness here, not rendering the block if property is '' or '0'.
Handlebars will render the block for '' and 0, but not other falsy values. This can cause some trouble when migrating templates.