I think the prophecy is more about foreshadowing the details and the procession of the events to follow. For example, we understand that the choices for the "Chosen One" sit basically between just Harry and Neville. The prophecy's outlined criteria clearly put these two boys interchangeably in the subject line, at least until referencing action based on the prophecy by LV. Because these boy's are the Schrodinger's Cat of prophecy subjects right now it is entirely likely that had Voldemort had a stronger opinion of Neville's family that he would have been the one that LV would have attacked, thereby making Neville the active subject of the prophecy in question. But, since he didn't..
"... and the Dark Lord will mark him as his equal, but he will have
power the Dark Lord knows not ..."
From this part we can safely gleam that the "power" that [He] will have will be something he didn't have up until the very moment LV tries to kill him the first time. which were Lily's Protection (arising from her loving act of ultimate sacrifice), becoming one of LV Horcruxes (something that has already been established within the books themselves as a process of murder, then placement of one's soul into a ready receptacle, living or otherwise. but is implied that it is a very fluid process and is highly unlikely to be a two spell type thing as Harry became one without LV's knowledge. so Harry has the ability to detect LV's presence and direct influence, and even has an indirect line and sometimes direct and coherent line to LV's mind.)
Further I believe that the last part of the prophecy;
"... and either must die at the hand of the other for neither can live
while the other survives ..."
References the situation in which one of the boys gets chosen, and the powers LV unknowingly bestows upon them, and how to correct it, rather than a physical and direct 'Neither can live with peace of mind and "Thrive" in life if the other still draws breath, no matter how destitute' as initially thought, but instead is about the chosen being a Horcrux: a vessel for part of LV's soul.
Now we already know that the act of creating a horcrux is considered darker than even the most forbidden magic, because of what it represents; breaking the soul apart, and the cost of doing so. and we also know that the nature of the soul is to be unified, which is why one must resort to dark magic in order to get it to do otherwise, and the whole point of doing it in the first place is to circumvent death (and they do a fine job doing that don't they?). But horcruxes by their very nature don't want to exist. They do simply because a particularly dark wizard willed and commanded them to do so. so we could surmise that their is a particular protection offered to horcruxes from the very act of containing a piece of one's soul.
Suppose then, for a second that it isn't imperative that LV be the one to kill Harry, for the sole reason that he's the one with the ability to destroy the part of his soul that lies within, as it may not be within his ability to do so (the books say that creating horcruxes is up there with some of the darkest magic a wizard could perform because it breaks the soul apart, but destroying it altogether may simply be one of those things that can't be done.), we could surmise from this that the soul fragments that are contained within the different items aren't destroyed, but rather released in much the same way they usually would be in a death of a person with a unified soul. So from this I would gather that LV doesn't have the ability to destroy the soul fragment that's inside harry, but instead the act of killing harry is the equivalent of murdering the original host, which wouldn't pose anyone a problem barring abnormal circumstances. The prophecy then would stress the importance of these concepts, implying that the very act of creating a horcrux within the subject of the prophecy is what guarantee's LV's downfall in the first place, but by that same token, also guarantee's harry's survival until then, providing him with protections only otherwise afforded to LV himself. (like the protection from death from LV'c various henchmen. How pissed do you think LV would have been if harry got killed by say Bellatrix, especially if LV knew his soul was contained within harry? And if he didn't know before he certainly would after harry's death.) But both knowing that as long as the other was alive, both would be in danger of dying at the hands of the other. I don't think it would have mattered much, if the outcome was that Bellatrix killed harry, as the vessel that contained LV's horcrux would still have been destroyed, but because is the grand scheme of things harry became the master of death, another power the Dark Lord was not aware of, they were both effectively immortal, but LV would be closer to death. The other thing is that DD was aware of a lot more than even he lets on in the books. It was even suggested that he has a Merlin type thing going on where he could somewhat accurately see into the future of others, but not so much his own future. Which explains the need for his elaborate plans that span nearly two decades. He has to account for his own actions in response to the futures he sees.
