You are most likely running into memory limitations built into the browser. Even though you may only have a few megs of KMZ data, that can decompress into much much more and Cesium also has lots of room for improvement when dealing with large amounts of entities (> 20000). While Google Earth can get away with brute forcing loading lots of data, browser based apps have to be a lot smarter about doing things (this is the problem 3D Tiles is eventually going to fix).
That being said, you can try temporarily increasing the amount of memory usable by Chrome to see if it helps you or not. First, be sure you are using the 64bit version of Chrome. 32bit apps only address up to 4GB of RAM (and depending on OS it can be lower). Chrome has artificial per-tab memory limits for the JavaScript engine of around 1GB on 32 bit and 2GB on 64 bit. As you can see, just running 64 bit will get you more memory.
Assuming that's still not enough, you can change the artificial limit by passing the --max-old-space-size to V8. This specifies the limit in megabytes. For example, if you want to raise the limit to 16GB you would run
chrome.exe --js-flags="--max-old-space-size=16384"
Don't set the value to higher than the amount of RAM on your machine. You also have to make sure chrome is not running in any capacity when you launch or else the command won't take. You can confirm this by checking the special chrome://version page, which lists command line arguments.
While this isn't an ideal solution overall, it might confirm that memory is the issue. If you can share one of the problematic KMZ files, we'd be happy to use it for performance testing when we try to optimize these cases in the future.