I've read somewhere that if you pour cheap vodka through a charcoal filter (one of those tap water filters) it will make it premium vodka, yet to test this.
n my experience, there is a difference. But with vodka, it's not as stark, because vodka is just kinda nasty, regardless of hoe good it is. But having a good quality makes for less severe hangovers. That's about it though, the actual drunk experience isn't better.
This isn't really entirely true, though it is to a point. The cheapest, shittiest vodka (or any liquor) is not distilled well enough or enough times to remove 100% of the methanol and other impurities resulting from fermentation. You will definitely get worse hangovers from the bottom shelf stuff than the better stuff. But once you hit a reasonable level of quality, the more expensive stuff tends to just taste a little less bad, it's not really going to be any different.