Logos engine vs Noet engine?

Is there any real difference? 

Not that I would know of it - which means: read about it on the forums, I never installed the Noet engine. From a screenshot on Noet.com it looks like the Guides section is disabled (as the Guides relate to bible exegesis. this probably makes sense).

is there a way to "sync" the libraries where whenever I buy and add something to one, it automatically gets added to the other program?

If you use the same email address to identify you as user for both, this will happen automatically anyway - you need to actively work against that by separating your accounts, if you want to keep the libraries apart. This means that your Noet installation takes the same amount of space on your system as your Logos installation, as it downloads every resource into both libraries.

Some people use this (more often with the Verbum engine, as I read it) to be able to run separate workspaces of Logos, such as to have more than one Library window or Guide open at a time.