Interesting discussion regarding using liquid oxygen (LOX) versus high concentration hydrogen peroxide (HTP) as the oxidizer in a rocket-propeled ALSR vehicle.
I have considerable experience with both. Obviously both are aggressively active oxidizers, one cryogenic and the other not. The cryogenic LOX causes design problems in delivering the oxidizer at high pressure into the rocket fuel system. Because of the low boiling temperature it must be pumped, not pressurized by air or nitrogen gases. The oxidizer system materials must be compatible with the very low temperatures, both for insulation and also material properties affected by the cryogenic temperature. A proper pump is quite complicated and costly. It really complicates what should be a relatively simple fuel/oxidizer delivery system.
Also, safety is an issue. I was involved in correcting the combustion problem that killed three NASA atronauts in the Apollo capsule during a static test. Using almost pure oxygen, a spark caused materials to burn violently which normally would not burn at all in air. Result, three dead astronauts and many months delay in the space program.
HTP is also a material that will cause fuels to burn vigorously. It must be handled carefully to keep the containers and delivery system clean. Proper material selection is also critical to avoid rapid decomposition - aluminum alloys, stainless steels, certain plastics - all common materials work fine. A simple blowdown oxidizer delivery system can be used and no cryogenic issues are there. It was used in the field at drag strips for several years with no major handling problems that I know of. Drag racers are not exactly expert at laboratory levels of cleanliness, but with minimal training had an exemplary safety record handling the HTP.
The Material Safety Data Sheets for both materials give a good comparison.