This is possible by ‘cheating’ with a block helper. This probably goes against the Ideology of the people who developed Handlebars.

Handlebars.registerHelper('ifCond', function(v1, v2, options) {
  if(v1 === v2) {
    return options.fn(this);
  return options.inverse(this);

You can then call the helper in the template like this

{{#ifCond v1 v2}}
    {{v1}} is equal to {{v2}}
    {{v1}} is not equal to {{v2}}