Burning methane also produces steam. Produces 891 kJ/mol, hydrogen 286 kJ/mol, methane has four hydrogen atoms that’d be 1144 kJ per what should the unit be in any case: Methane produces less heat per unit of produced water than hydrogen (the hydrogen first needs to get ripped off the carbon). Those ovens burn dryer than your current gas oven.

Never used steam when making pizza, they’re not in there long enough for steam to make a difference. For bread it’s indispensable to get a proper crust, though.