If I zip tiffs using Image Processor or Image Processor Pro, the file gets zipped but not the layers. That means the zipped tiffs are much bigger than the psds. Zipping the layers manually is very tedious, but gets the size down to about the same or slightly less than a psd. It seems to me that selecting zip for compression should zip everything by default. It doesn't seem to.
You could record an action and then use File>Automate>Batch instead of Image Processor Pro.
It's possible the code could be modified for Image Processor Pro and/or Image Processor, but that's probably best asked on the photoshop scripting forum: