How do I divide taxonomy term pages by content type?
A couple approaches come to mind, I will outline the one that does not use panels.

Start by overriding the default taxonomy page by enabling the one that comes with views.  At this point you will have the same behavior as the default taxonomy pages.

Clone the default taxonomy view and disable the clone (this is case you want to restore the view).

Now back to the taxonomy view

Remove the existing two contextual filters  (not this means the depth feature will no longer be available)

Add a contextual filter on "Content: Has taxonomy term ID"
Add another on "Content: Type".

Change the path to "taxonomy/term/%/page" (for page use the content type machine name you want for this tab)

Change "menu" setting to "default menu tab" 

(A) Clone the "Page" display, I gave by clone the name of the content type for the tab

(B) Change the path so "page" is replaced with the next content type you want.

(C) Change "menu" setting to "menu tab"

Repeat (A) (B) and (C) for each content type/tab