Quote - > Quote - I fear the only true answer is no.

You could share parts and pieces, but whole scenes can not be transferred between both apps. (and certainly not maintain all its functionalities, materials, rigging, Subd, to name a few are different and not 100% interchangable)

That was my suspicion. What about one character and his or her clothes + Props? Or would it at least be possible to bring over the character, the clothes, and the props separately?

The information you are given is not entirely correct. Much depends on what it is that is in the scene in the first place. Or what is in the DAZ Studio scene.  Assets are easy.

Now if your figures in Poser are rigged with Poser8+ (Most are not) they will not work, further Poser and DS Dynamics are not cross compatible. Within those restrictions and bearing in mind that render engines are different so shaders will have to be translated, as long as you turn off save "external binary morphs" in preferences, then DAZ Studio reads CR2, PP2, pz2, etc. files just fine. Even scene files (PZ3) go across just fine. 

Going the other way can be a little tougher. Again bearing in mind that DSON assets require DSON importer for Poser to use in Poser. And DS does not export PP2 or PZ3 format.

DAZ Studio will export characters that are created with Poser rigging (and yes, DAZ Studio can create figures with Pre Poser 8 rigging just fine) as CR2 files, and can export pz2 files for morph injections, poses, and basic materials just fine. DS can export static props as OBJ at Poser scale which can be imported into Poser and easily turned into a PP2 files.

 

So the situation might not be as dire as you thought.