Well, I have attended a conference on water conservation in 2014, there was an interesting discussion about the purity of water and water storage. Your question reminded me of that.
To answer your question, We have to make it clear, on how long are we gonna store the water for, we all know that basic material for glass is silica and for plastic it is carbon. Silica is more stable than carbon so it doesn't oxidize soon, carbon too is stable but when compared to the silica carbon relatively oxidizes in a long run. Resulting in browning of the plastic and becoming greasy.
So, if you are storing just for days, or weeks (after opening), it is fine to use plastic. Glass is always a better option.