The problem here lies in definitions. Some people have different definitions of what an OBE is and encompasses. Summerlander, you deliver a definition with mode1/2 and "the phase", but it's your own (or rather leaned on Radruga's models?), not used by others. So many people who have different definitons or use categories differently might not be able to relate to it. Don't get me wrong, I actually like your model, but it is actually one way (belief?) of looking at things only.
As to the question: normally I'd go for LD=OBE, but as said, that depends then on "my" definition of them, they might not be exactly what is presented here by your post or Radruga's teachings. So it is still difficult to vote for me. (I'm on the fence and thus have not yet cast a vote).
Well, actually I don't have a definition for a Lucid Dream anymore, if I think right about it. I just differentiate between the non-lucid/dream state and the lucid state. So it is all about the "state continuum" (that might indeed come near to your described "phase" in a way).
And both, for me, are real. They are "realties" to be experienced within one super-reality, so to speak. Some still argue that dreams are "less real" which I decidedly oppose all the time. I even take more or less the occultist view now, that poses that dreams are just filtered-down (and thus scrambled) memories of experiences in higher states of our multidimensional (higher) self, which we mostly cannot really understand due to their complexity.
I think, not just from other authors' but also from my own experiences now, that in dreams/non-lucid state you are nearer to your sub- or superconscious (which esotericists call Higher or Monroe called Total Self / I-there). My dreams tell me the same story, I have the impression now that I even get better insights about (or from?) my (higher) self from dreaming.
Then there is varying degrees of lucidity in-between when you flicker between lucid and non-lucid. So there is no clear-cut boundary.
On the other side of the continuum, the complete lucid/self-conscious analytical state (which I call lucidventure when not experienced in betawaves-brainstate / the 'physical') is more externally geared, away from your Higher Self / subconscious. Your conscious / lucid incarnated ego-self is then in full control and experiences the (physical, astral or whatever) environment, collects data from there and ... well ... lives and learns, all for the benefit of the Higher Self.
So, dreams and lucidventures (OBEs if you like) are in the same continuum of consciousness, you just change focus and state on this wide-ranging continuum, voluntarily or involuntarily. So yes, dreams and lucidventures they are actually THE SAME. A 'lucid dream', however, does not fit into this model for me anymore. For me there are either dream adventures or lucidventures / lucadventures.

Both are valid and valuable experiences for me because either way can lead to precious insights and even validations of some sort. I had now certain validations as pre-cogs and clairvoyant insights in "normal" dreams, but also a kind of telepathic manifestation and ensuing validation from a lucadventure ("OBE / AP" or I guess you'd call it Mode2 due to the telepathic thing). Therefore I do not believe from my experiences (and that's what you asked for: own experiences) that one side (state/focus) of the same thing (continuum) is "better" or "more real" than the other.