as far as lore goes syndra, as a child. sucked every last drop of power (and presumably, life essence) out of the ghost-willow, a tree which shares similarities with the god-willow from Ivern's lore. so a mystical 8000+ year old tree, and promptly let her anger condense that magic in her ever-iconic dark spheres.
in her years under tutelage from konnigen (syndra's mentor) her power eventually grew so much that they started to warp reality. until the 'spirit of the land' intervened and subdued syndra in the dreaming pool for an undisclosed amount of time.
ryze on the other hand has travelled with his master in search of the world runes in order to lock them away: upon his master's passing he inscribed himself with runes which altered him (hence the blue skin) and extended his life so that he could continue his work.
despite this the ryze:call to power video shows that he is still capable of being harmed by even small arms such as a dagger.
now the void creature that ryze defeated seemed like vel'koz, but in reality is one of the frozen watchers (an creature that actually originated from the void) and was able to best it by unleashing his full power, his method was to overload the watcher with arcane energy and he was succesful tough quite exhausted afterwards.
now having talked about their respective levels of power, it is clear that syndra wins this with ease - warping reality means you have enough power to do, really just about anything.
moving on to the mental aspect: i'd say that ryze is a clear winner here. he is capable of making people trust him (despite their fear of his power and his looks) including several champions (MF, Sona and Nasus.) not only that, he is capable of withstanding the corruptive power of the world runes, which almost instantly corrupted khegan (Brand)
syndra on the other hand seems to posses mostly negative emotions: no real wonder with her childhood. which makes her less easy to approach as well as easy to anger. (and anger leads to making mistakes)
in other words:
who's more powerful? 
who is more knowledgeable? 
who would win in a battle? depends.
if it was a chance meeting no doubt. she could crush with her will alone.
if both had an opportunity to prepare? , he has more knowledge and experience.
i hope that satisfies your question.
That's all.
