This can very become an esoteric debate that focuses on super micro-analytical conversations about contamination, bottle degradation and health risk. For all practical purposes there is no difference between glass or plastic. One can debate the pros and cons of the sturdiness of glass versus the weight, and the pros and cons of lightweight plastic versus the eventual chemical breakdown of the bottle, however, for the lifetime of you and I, storing water in glass or plastic makes no difference. You could also store it in 316 stainless steel bottles if you so chose.
There is one caveat, however. My answer pertains to storing water that has been properly bottled by a validated bottled water company. Those companies have sanitization processes for both the bottles and the water. When they seal a bottle for sale, it is safe, harmful contaminant free and, very suitable for long-term storage.
Okay, there is one more caveat. Once the bottle has been opened, all bets or off. Once opened, the water will be unprotected from atmospheric and physical contamination. At the point any bottled water is open, it’s half-life of being safe to drink begins to diminish.