Well, it's FAR from "not the cheapest" (that's what "substantially more" means). As far as I can tell, it's one of the most expensive, charging almost double what the discount pharmacies charge.
For years many have recommended Chula Bhaesaj Drug Store on Rama IV. I've used it and found it to offer both the largest inventory and probably the lowest prices. You can find pretty much any drug there, things that the little Sukhumvit pharmacies won't have. The only drawback is that the lines can be a bit long, as it's not far from a major hospital.
https://www.thebigchilli.com/feature-stories/bangkok-pharmacy-with-a-cure-for-a-tight-budget
It's a short walk from the Sala Daeng BTS station, and convenient to Patpong