"Obviously you'll lose more at deeper depths."
Not necessarily. If an LP hose (or its O-ring(s)) blows or you free-flow, then you would lose more at deeper depths, as the pressure (and therefore, the quantity of air) increases parallel to ambient pressure. However, if an HP hose (or its O-ring(s)) or a valve O-ring (i.e. at the yoke) blows, you'll be losing air from the tank pressure to ambient, which is greater at deeper depths, meaning the delta-P across the breech (and by relation, the flow rate) is inversely related to ambient pressure. Although I do not believe this relationship is significant for recreational diving (I would simply consider HP blowouts to be constant rate vs. depth), it does run counter to the obvious rule that applies to LP blowouts.
As far as draining a tank faster if an LP hose bursts vs. the HP hose, the LP hoses are designed to allow as much air through them as possible with minimal restrictions (you want to be able to hoover the tank if you need to, after all). The HP hoses, on the other hand, are normally equipped with a very small (almost pinhole) orifice on the end that screws into the first stage, as there is no need for large flows through the hose. In the event of an HP hose (or SPG) blowout, this very small orifice restricts the flow to a mass flow rate much lower than that of an LP hose blowout.