There are some people who claim there is a relationship between loot and leaderboard or prestige and some who claim there isn't. We can't know for certain whether or not there is a relationship between prestige and the items you get from store chests unless we have enough data to find such a correlation, and as far as I know no one has attempted to go beyond hearsay to figure it out.
As someone who has opened 400 large chests at different prestige levels and even opened 100 while at 20th place on the leaderboard, I have an opinion on this as well (you can see video and results in thread "100 large chests"). I may be wrong because 400 chests with chests opened at different prestige levels and leaderboard rankings is not nearly enough of a sample size, so I am not saying that I know I am right, just that in my opinion it is not likely for prestige or leaderboard ranking affects loot.
I would also like to bring to attention the fact that to program a relationship between loot from store chests and prestige or leaderboard would require a very sick mind. Who really wants to punish and reward people based upon prestige, something that is basically a counter of your achievement progress and how many times you have promoted characters, or upon leaderboard ranking, which would probably result in punishing tens of thousands of players and only reward the top 100 or maybe less? You'd have to be a super @$$hole or a despair demon to come up with the idea to program store chests to be affected by leaderboard or prestige.