@xxgin: Ok, it can be confusing, mostly because Geoff Johns is a hack writer. Anyways, here's the break down in power levels and an attempt at explaining why.
Zero Hour Parallax >Hand of God Ion >Sinestro CORPS War Parallax =(roughly) Sinestro CORPS War Ion and all Sinestro CORPS War entities >White Lantern
Now I put the white lantern at the bottom because generally the power output seems to be about the same as the other CORPS rings. However, the white lantern ring shows special abilities such as being super effective against black lanterns, creating constructs capable of harming the Third Army, restoring life, and healing. In terms of raw power though, I don't see the white lantern ring as being much more powerful than any of the other CORPS ring.
Now Zero Hour(ZH) Parallax is the strongest because he consumed all the energy of the central power battery(CPB) on OA. The entire power of the corps was centered in one being. Additionally he later absorbed "cronal energies" from the time stream left over from the Anti-Monitor during Crisis on Infinite Earths(COIE). Also, through retroactive continuity(retcon) (feel free to ask about retcons if you're not yet familiar with that phrase) he also possessed the Parallax fear entity. ZH Parallax destroyed the entire universe an infinite amount of times over. He destroyed the universe in every moment of time from the end of time back to the beginning.
Hand of God(HOG) is simply what the fans call Kyle Rayner as Ion when he first became Ion. HOG Ion is the second strongest because he possessed almost the same abilities as ZH Parallax. When Parallax died reigniting the sun during Final Night (a mini-series in which DC's sun was extinguished) vast quantities of the energy Parallax absorbed from the CPB were left in the sun. Kyle Rayner absorbed these powers and called himself Ion. He was able to be a virtually anywhere in the universe at once. It was implied that nothing was beyond his power and that his power even surpassed that of the Spectre. Also, through retcon he possessed the Ion will power entity.
NOW, we get to the Green Lantern Rebirth (a story which saw the resurrection of Hal Jordan). Rebirth (written by Johns) established that "Parallax" wasn't just a name that Hal Jordan took for himself when he turned into a villain and tried to recreate the universe. Parallax was actually an ancient entity. Parallax was the avatar of fear. Parallax had possessed Hal Jordan and that's what lead to him turning into a villain. Later on in Sinestro CORPS war and during the War of Light, Johns would establish that each part of the emotional Spectrum had it's own ancient entity which acted as an avatar for that particular CORPS. For the Green Lanterns, their avatar was Ion. Through a retcon, it was written that when Kyle originally became Ion, it was because he had become possessed by the Ion entity.
Lol, still with me?
So, during the Sinestro Corps War and onward whenever someone got possessed by one of the emotional entities, be it Parallax or Ion, they got a boost in power. However, this boost in power was nowhere close to when we originally saw Parallax or Ion because originally both of them had HUGE additional power boosts on top of the entities. Parallax had all the power from the CPB and the cronal energies from the Anti-Monitor. Ion had all the left over power from the CPB from when Parallax killed himself reigniting the sun.
Hope that helps.
Edit: OH SNAP. Lol, I complete forgot the original question was Volthoom vs ZH Parallax. As said above ZH Parallax stomps because he display MUCH Higher Power levels than Volthoom (i.e. being able to destroy, manipulate, and create all of reality). So, to Volthoom into my original breakdown
ZH Parallax > HOG Ion > Volthoom > People possessed by emotional entities during Sinestro Corps War and onward > White Lantern
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