How can I uniquely union two array of objects?

Concat and use Array#filter with a helper object to remove duplicates:

var array1 = [{"a":1,"b":"first"},{"a":2,"b":"second"}];

var array2 = [{"a":3,"b":"third"},{"a":1,"b":"fourth"}];

var result = array2.concat(array1).filter(function(o) {  
  return this[o.a] ? false : this[o.a] = true;
}, {});

console.log(result);

If ES6 is an option you can use a Set instead of the helper object:

const array1 = [{"a":1,"b":"first"},{"a":2,"b":"second"}];

const array2 = [{"a":3,"b":"third"},{"a":1,"b":"fourth"}];

const result = array2.concat(array1).filter(function(o) {  
  return this.has(o.a) ? false : this.add(o.a);
}, new Set());

console.log(result);

If you want to use an arrow function, you can't use the thisArg of Array.filter() to bind the Set as the this of the function (you can't bind this to arrow functions). You can use a closure instead (attribute for the method goes to @NinaScholz).

const array1 = [{"a":1,"b":"first"},{"a":2,"b":"second"}];

const array2 = [{"a":3,"b":"third"},{"a":1,"b":"fourth"}];

const result = [...array2, ...array1]
  .filter((set => // store the set and return the actual callback
      o => set.has(o.a) ? false : set.add(o.a)
    )(new Set()) // use an IIFE to create a Set and store it set
  );

console.log(result);