I don't have a 22" WSM.
My thinking is I believe the food maybe several pounds or more of meat your are cooking, consums more energy, than heating the addition space/volume of the bigger unit.
In other words, yes it takes more fuel to heat the 22" than the 18". If you look at the total, energy/fuel comsumption, the biggest portion of that would be the food assuming you use a dry water pan.
Now if you put water in the pan, the additional volume of water on the 22" plus the additional volume/space in the 22" might be a slightly different story. Plus the added capacity/meat you can put on the 22", of course would require the larger ring.
Just my 1.5 cents worth.