On an electric stove, does the smaller burner produce fewer BTUs than the larger burner

A regular electric oven uses a large coiled resistor as a heating element. A large electric current is passed through this element which generates heat, similar to the tungsten filament of an incandescent light bulb.

An induction stove doesn't actually generate heat itself, but rather induces it the pot or pan. It does this using a rapidly oscillating magnetic field. This field induces an electric current in a ferromagnetic pan which generates heat, thus heating the food.

Induction stoves are faster, safer, and more energy efficient than traditional electric stoves. It requires significantly less electricity to create the magnetic field than it does to drive enough current through a resistor to make it heat up. They are safer because they don't actually generate heat themselves. After taking a pot off the "burner" (glass surface) it quickly begins to cool.

With regards to differences in the cooking process, there's not much. You just need to be aware that it heats up much more quickly and cools down much more quickly than a traditional electric stove. It does affect your choice of pans however. All aluminum pans will not work, nor will some lower quality stainless steel ones. If a magnet sticks to the pan then it will work just fine. The pan must also have a flat bottom to make full contact with the surface.

Basically you need a pan that is clad on the bottom. What this means is that there are usually three layers. Normally steel | aluminum or copper | steel. These pans will conduct and heat the most evenly on the bottom. Even with one of these however, you're still asking a lot to evenly heat 12 inches on 7 inches.

If its really important to you, you could consider a separate high end stand alone large burner. This one may be large enough for example.