This method is how I have it setup personally, and i havent ran across the issue of it not updating. Did you experience this issue elsewhere with other items other than the hopper? Since this method relies on using a comparator to get a 2 redstone tick out, if the comparator isnt getting an update, it should be affecting the chest methods as well unless the hopper has something oddly issued around it in your particular setup.
Sorry I missed this post Daniel! No, the way the comparator works, is that it emits a redstone signal based on the total number of items in the container out of the total number of possible items in the chest. The stack size also affects this value, meaning if you have a hopper with only one item in it that stacks up to 64, the maximum item count is (5*64), and it would send a signal out based on that % of it, if however you have eggs in there, which only stack up to 16, and you have empty spaces elsewhere, the max is (16+4*64).