Hydrogen has become recognized as a 'gourmet fuel' for cooking. Hydrogen emits absolutely zero toxic by-products when burned, the main by-product (besides heat) is, of course, steam. Although hydrogen is not the best fuel for baking (things come out a little soggy without some simple oven modifications), hydrogen is totally unsurpassed for cooking any type of steamed dish.

One of the big differences between propane and hydrogen is availability. Price comparisons are difficult because the price of hydrogen can vary so greatly. Propane can only be purchased (at fairly stable prices) from a few sources. It would probably cost more if you bought your hydrogen in pressurized tanks from a local welding supplier (for instance).

It's conceivable (depending on location) that a single solar panel could produce all the hydrogen needed for household cooking purposes. That's cooking for FREE after the initial investment in the solar panel, electrolyzer, storage and conversion from propane to hydrogen.