Why doesn't the pagination work for a comment type, but it works for the other one?
If you have more than one listing on a page, the pager ID for each needs to be different. This applies to views, but also comment lists.

The way to change this is under your content type's display settings (admin/structure/types/manage/MYTYPE/display). For the comment fields, click on the gear icon and you should see this configuration option:



So long as each comment type uses a different ID, the pagers should work independently of each other.