It's the same engine, with superficial tweaks, and ported to DX11. However, DX11 has nothing to do with the engine itself, it's like saying a book originally written in Japanese was written in English just because it was translated over. Microsoft is pushing devs to DX11 to force XP (and hopefully 32-bit windows with it) out the door.
http://gamerant.com/black-ops-2-doesnt-need-new-engine-dyce-149032/
The biggest clue is that the X360 and PS3 are the primary dev platforms, platforms which lack entirely anything to do with DX11-specific features. People would freak out if the PC version had any notable differences other than resolution options over the console versions, and you'll notice that there is no difference between the PC and console versions of Blops2. Hence, no DX11 features at all (otherwise the PC version would feature graphical elements that would be impossible on console).
Is this a bad thing? Well from a business standpoint, when your primary platforms, the consoles, outsell the PC versions something like 50-1, we're lucky to see PC ports of the COD games at all. And with the consoles, there's pretty much no reason to even try a new engine, the COD games are as good as they're going to get on ancient hardware and still hit 60fps. From a PC gamer perspective, they are antiquated as hell, but if someone enjoys them, more power to em.
What is dishonest is trying to make it sound like Blops2 is anything more than
minor tweaks on the COD4 engine, just like it has been all along. That's simply the truth.