A stereo reverb will correctly cross information between the right and left channels. A dual mono reverb treats both channels as separate. The rationale is simple - reverb was originally intended to spatially locate a sound - that is to say, to put it in an environment. If a sound is in stereo, it is itself spatialized with respect to the listener - thus the two channels are coherent with respect to each other and have a combined “meaning” if you will. Thus, the reverberation should take that into account as if the spatialized sound were itself coming from a single source somewhere in the notional environment, thus both channels contain relevant information to integrate into the greater whole, and will affect each other.
Dual mono is not stereo - it’s just two channels being processed more or less simultaneously, thus none of these presumptions apply.
Eventide are one of the few to really comprehend this, and I love the way their stereo reverbs do, in all cases I can recall, correctly cross-connect the two channels’ reverb response, but not the original dry signals. IMO, this is the “right way” to do it, but not all reverb units do - many (most?) sum the inputs to mono before applying reverb (sometimes just returning that mono wet reverb on both of the two-channel dry signal outputs), some are really just dual mono under the hood.
