The density difference is minor. Slightly more density for H2O2 (1.387 vs 1.14) but nearly irrelevant. The major advantage is the oxidizer tank would be lighter since you need no insulation. The talk H2O2 is safer than LOX is bollocks. HTP can be dangerous to handle if you do not know what you are doing. There were several accidents with H2O2 in the late WW2 period when they were trying to use it in submarines. After WW2 when it was used in torpedos there were several fatalities fueling torpedos up in the factory.
The danger with handling HTP is a big reason why you seldom see it used in those applications anymore. All it takes is some metal flakes in the fuel tank leftover from the milling process that no one noticed, and you get a rampant fuel decomposition, and explosive compression with possible ignition event.
I doubt LOX has any Isp advantage in real terms over HTP since if you look at it, the HTP is just H2 and O2. The major issue with H2O2 is that they typically decompose it with a catalyst, I think with a platinum catalyst, before ignition with Kerosene and that takes more weight than using an hypergolic starter cartridge which is what they typically use with LOX.