Use the names as a checklist, not a ranking
Stone, Gold, Iron, Diamond and Purple are real pickaxe names attached to the game. Badge order does not tell us which is strongest or what each one costs.
When a new pickaxe appears in your server, read the requirement and stat text shown by the game before spending Wins or leaving your current stage. The public Roblox description confirms that pickaxes are part of progression, but it does not publish their exact numbers.