第二个方法可以对所发送的消息进行判断，从而进行不同的处理。如果没有分类处理的需求，发一个空消息就够了。

从源码看
先是sendEmptyMessage(int what)

    public final boolean sendEmptyMessage(int what)
    {
        return sendEmptyMessageDelayed(what, 0);
    }

再点进sendEmptyMessageDelayed(what, 0)

    /**
     * Sends a Message containing only the what value, to be delivered
     * after the specified amount of time elapses.
     * @see #sendMessageDelayed(android.os.Message, long) 
     * 
     * @return Returns true if the message was successfully placed in to the 
     *         message queue.  Returns false on failure, usually because the
     *         looper processing the message queue is exiting.
     */
    public final boolean sendEmptyMessageDelayed(int what, long delayMillis) {
        Message msg = Message.obtain();
        msg.what = what;
        return sendMessageDelayed(msg, delayMillis);
    }

从sendEmptyMessageDelayed(int what, long delayMillis)方法中
可以看到what参数赋给了obtain出来的Message对象

再从obtainMessage(1,data)的源码中看

    /**
     * 
     * Same as {@link #obtainMessage()}, except that it also sets the what and obj members 
     * of the returned Message.
     * 
     * @param what Value to assign to the returned Message.what field.
     * @param obj Value to assign to the returned Message.obj field.
     * @return A Message from the global message pool.
     */
    public final Message obtainMessage(int what, Object obj)
    {
        return Message.obtain(this, what, obj);
    }

方法返回Message.obtain(this, what, obj),接着继续看obtain(this, what, obj)

    public static Message obtain(Handler h, int what, Object obj) {
        Message m = obtain();
        m.target = h;
        m.what = what;
        m.obj = obj;

        return m;
    }

方法里面Message也是通过obtain来获取的，不过这里还将obj对象赋给了Message。
sendToTarget()的源码中的target是Handler，就是调用了sendMessage()方法

    /**
     * Sends this Message to the Handler specified by {@link #getTarget}.
     * Throws a null pointer exception if this field has not been set.
     */
    public void sendToTarget() {
        target.sendMessage(this);
    }

    public final boolean sendMessage(Message msg)
    {
        return sendMessageDelayed(msg, 0);
    }

sendEmptyMessage(int what)和obtainMessage(int what, Object obj).sendToTarget()
最大的不同就是没有了Object这个对象

参考：
Handler 的sendEmptyMessage(int what)和sendMessage（Message msg）有啥区别？
Handler sendMessage 与 obtainMessage (sendToTarget)比较

没啥太大不同，第一个是发送空消息，第二个是从消息池取一个消息发送。

没什么不同，只是提供了多样的API给你用，你怎么用的习惯就怎么用