Quantity Breaks applies discounts when specified quantities (and above) of specified products are added to the cart. So for example, X quantity of Y product in the cart will discount each quantity by Z. You're able to allow customers to mix and match products where the quantities are combined together to trigger a quantity based discount. Quantity Breaks will also show a grid on the product page of selected products that illustrates what quantities will result in what discounts.
Bundles applies discounts when all specified products in a bundle are added to the cart. So for example, if product X and product Y are in the cart, then apply discount Z to each of them. Quantity is only a factor in the sense that each product in each completed bundle set in the cart is discounted, and if one product of the bundle has more quantity in the cart then the other bundle products, then that extra quantity won't be discounted, since that extra quantity isn't part of a completed set. The app will output a bundle widget on all product pages of the products that are selected to be in the bundle, and the customer is able to add the entire bundle to the cart through any product pages bundle widget.
It's important to note that with Product Bundles, the same products or collections cannot be bundled with each other, whereas with Quantity Breaks you can add multiple of instances of the same product to the cart to trigger a quantity based discount.