Как отследить изменение размера div'ов?

Самое простое решение:

var blockWidth = $('.block').outerWidth(); 
$(window).resize(function() { 
  if (blockWidth != $('.block').outerWidth()) { 
    console.log('resized') 
  } 
});

.block { 
  max-width:300px; 
  height:100px; 
  background:#000; 
}

<script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.1/jquery.min.js"></script> 
<div class="block"></div>

Конкретно на вашем примере:

var blockWidth = $('#test_div').outerWidth(); 
$(window).resize(function() { 
  if (blockWidth != $('#test_div').outerWidth()) { 
    console.log('resized') 
  } 
});

.block { 
  max-width: 300px; 
  height: 100px; 
  background: #000; 
}

<script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.1/jquery.min.js"></script> 
 
<div id="test_div" style="width: 100%; min-height: 30px; border: 1px dashed pink;"> 
  <input type="button" value="button 1" /> 
  <input type="button" value="button 2" /> 
  <input type="button" value="button 3" /> 
</div>

Существует очень эффективный метод определения того, был ли изменен размер элемента.

http://marcj.github.io/css-element-queries/

Код библиотеки:

/**
 * Copyright Marc J. Schmidt. See the LICENSE file at the top-level
 * directory of this distribution and at
 * https://github.com/marcj/css-element-queries/blob/master/LICENSE.
 */
;
(function(root, factory) {
  if (typeof define === "function" && define.amd) {
    define(factory);
  } else if (typeof exports === "object") {
    module.exports = factory();
  } else {
    root.ResizeSensor = factory();
  }
}(this, function() {
  // Make sure it does not throw in a SSR (Server Side Rendering) situation
  if (typeof window === "undefined") {
    return null;
  }
  // Only used for the dirty checking, so the event callback count is limited to max 1 call per fps per sensor.
  // In combination with the event based resize sensor this saves cpu time, because the sensor is too fast and
  // would generate too many unnecessary events.
  var requestAnimationFrame = window.requestAnimationFrame ||
    window.mozRequestAnimationFrame ||
    window.webkitRequestAnimationFrame ||
    function(fn) {
      return window.setTimeout(fn, 20);
    };
  /**
   * Iterate over each of the provided element(s).
   *
   * @param {HTMLElement|HTMLElement[]} elements
   * @param {Function}                  callback
   */
  function forEachElement(elements, callback) {
    var elementsType = Object.prototype.toString.call(elements);
    var isCollectionTyped = ('[object Array]' === elementsType ||
      ('[object NodeList]' === elementsType) ||
      ('[object HTMLCollection]' === elementsType) ||
      ('[object Object]' === elementsType) ||
      ('undefined' !== typeof jQuery && elements instanceof jQuery) //jquery
      ||
      ('undefined' !== typeof Elements && elements instanceof Elements) //mootools
    );
    var i = 0,
      j = elements.length;
    if (isCollectionTyped) {
      for (; i < j; i++) {
        callback(elements[i]);
      }
    } else {
      callback(elements);
    }
  }
  /**
   * Class for dimension change detection.
   *
   * @param {Element|Element[]|Elements|jQuery} element
   * @param {Function} callback
   *
   * @constructor
   */
  var ResizeSensor = function(element, callback) {
    /**
     *
     * @constructor
     */
    function EventQueue() {
      var q = [];
      this.add = function(ev) {
        q.push(ev);
      };
      var i, j;
      this.call = function() {
        for (i = 0, j = q.length; i < j; i++) {
          q[i].call();
        }
      };
      this.remove = function(ev) {
        var newQueue = [];
        for (i = 0, j = q.length; i < j; i++) {
          if (q[i] !== ev) newQueue.push(q[i]);
        }
        q = newQueue;
      }
      this.length = function() {
        return q.length;
      }
    }
    /**
     *
     * @param {HTMLElement} element
     * @param {Function}    resized
     */
    function attachResizeEvent(element, resized) {
      if (!element) return;
      if (element.resizedAttached) {
        element.resizedAttached.add(resized);
        return;
      }
      element.resizedAttached = new EventQueue();
      element.resizedAttached.add(resized);
      element.resizeSensor = document.createElement('div');
      element.resizeSensor.className = 'resize-sensor';
      var style = 'position: absolute; left: 0; top: 0; right: 0; bottom: 0; overflow: hidden; z-index: -1; visibility: hidden;';
      var styleChild = 'position: absolute; left: 0; top: 0; transition: 0s;';
      element.resizeSensor.style.cssText = style;
      element.resizeSensor.innerHTML =
        '<div class="resize-sensor-expand" style="' + style + '">' +
        '<div style="' + styleChild + '"></div>' +
        '</div>' +
        '<div class="resize-sensor-shrink" style="' + style + '">' +
        '<div style="' + styleChild + ' width: 200%; height: 200%"></div>' +
        '</div>';
      element.appendChild(element.resizeSensor);
      if (element.resizeSensor.offsetParent !== element) {
        element.style.position = 'relative';
      }
      var expand = element.resizeSensor.childNodes[0];
      var expandChild = expand.childNodes[0];
      var shrink = element.resizeSensor.childNodes[1];
      var dirty, rafId, newWidth, newHeight;
      var lastWidth = element.offsetWidth;
      var lastHeight = element.offsetHeight;
      var reset = function() {
        expandChild.style.width = '100000px';
        expandChild.style.height = '100000px';
        expand.scrollLeft = 100000;
        expand.scrollTop = 100000;
        shrink.scrollLeft = 100000;
        shrink.scrollTop = 100000;
      };
      reset();
      var onResized = function() {
        rafId = 0;
        if (!dirty) return;
        lastWidth = newWidth;
        lastHeight = newHeight;
        if (element.resizedAttached) {
          element.resizedAttached.call();
        }
      };
      var onScroll = function() {
        newWidth = element.offsetWidth;
        newHeight = element.offsetHeight;
        dirty = newWidth != lastWidth || newHeight != lastHeight;
        if (dirty && !rafId) {
          rafId = requestAnimationFrame(onResized);
        }
        reset();
      };
      var addEvent = function(el, name, cb) {
        if (el.attachEvent) {
          el.attachEvent('on' + name, cb);
        } else {
          el.addEventListener(name, cb);
        }
      };
      addEvent(expand, 'scroll', onScroll);
      addEvent(shrink, 'scroll', onScroll);
    }
    forEachElement(element, function(elem) {
      attachResizeEvent(elem, callback);
    });
    this.detach = function(ev) {
      ResizeSensor.detach(element, ev);
    };
  };
  ResizeSensor.detach = function(element, ev) {
    forEachElement(element, function(elem) {
      if (!elem) return
      if (elem.resizedAttached && typeof ev == "function") {
        elem.resizedAttached.remove(ev);
        if (elem.resizedAttached.length()) return;
      }
      if (elem.resizeSensor) {
        if (elem.contains(elem.resizeSensor)) {
          elem.removeChild(elem.resizeSensor);
        }
        delete elem.resizeSensor;
        delete elem.resizedAttached;
      }
    });
  };
  return ResizeSensor;
}));

Эта библиотека имеет класс ResizeSensor, который можно использовать для определения размера.

Он основан на событиях, поэтому он чертовски быстро определяет и не нагружает процессор.

Пример:

new ResizeSensor(jQuery('#divId'), function(){ 
    console.log('content dimension changed');
});

Пожалуйста, не используйте плагин resize для jQuery, поскольку он использует цикл setTimeout() для проверки изменений.