constructor is a regular property of the prototype object (with the DontEnum flag set so it doesn't show up in for..in loops). If you replace the prototype object, the constructor property will be replaced as well - see this explanation for further details.
You can work around the issue by manually setting Obj2.prototype.constructor = Obj2, but this way, the DontEnum flag won't be set.
Because of these issues, it isn't a good idea to rely on constructor for type checking: use instanceof or isPrototypeOf() instead.
Andrey Fedorov raised the question why new doesn't assign the constructor property to the instance object instead. I guess the reason for this is along the following lines:
All objects created from the same constructor function share the constructor property, and shared properties reside in the prototype.
The real problem is that JavaScript has no built-in support for inheritance hierarchies. There are several ways around the issue (yours is one of these), another one more 'in the spirit' of JavaScript would be the following:
function addOwnProperties(obj /*, ...*/) {
for(var i = 1; i < arguments.length; ++i) {
var current = arguments[i];
for(var prop in current) {
if(current.hasOwnProperty(prop))
obj[prop] = current[prop];
}
}
}
function Obj1(arg1) {
this.prop1 = arg1 || 1;
}
Obj1.prototype.method1 = function() {};
function Obj2(arg1, arg2) {
Obj1.call(this, arg1);
this.test2 = arg2 || 2;
}
addOwnProperties(Obj2.prototype, Obj1.prototype);
Obj2.prototype.method2 = function() {};
This makes multiple-inheritance trivial as well.