The Advantium 120 convection oven function (that uses a conventional heating element and a fan) is actually the same as the 240. The microwave in the 240 is slightly more powerful but similar. The major difference is with the speedcook mode that uses halogen lights along with microwaves to cook, allowing the A240 to cook almost as fast as a microwave but retaining most of the cripsier texture usually only possible with a standard oven. The 240v version, besides being twice the voltage, is also twice the amperage (30 amps instead of 15), so it has access to up to 7200 watts instead of only 1800. As GE points out, this allows the speedcooking on the 240 to be twice as fast as the 120. What GE doesn't make clear is that the A120 also relies much more on microwaves to cook than the A240 does (check the published specs for the differences, noting the halogen lamps are much higher wattage in the 240). So food speedcooked in the A120, besides taking twice as long to cook, have a bit more of that soggy microwaved texture, although it can still cook noticeably better than a microwave for many foods. So basically if you want the Advantium mostly for the conventional cooking mode and/or as a microwave oven, the A120 works fine and about as good as the A240; but for the speedcook mode the A240 is substantially faster and cooks better.

Correct that only the 120v Advantium is rated for installation under a countertop, and only the 30" wide version, not the 27". I think some other brands (Miele? Electrolux? Jenn-Air?) allow installation under a countertop with their 240v speed ovens; check the installation instructions. There's also the Advantium 240v over-the-cooktop model, which works very well in all cooking modes, though the oven isn't as deep front-to-back as the wall-oven versions and the exhaust fan isn't as powerful as a good separate range hood.

The primary difference is in the speed and interior light function:

240 volt Advantium

• 4x-8x faster than conventional cooking
• Can
  have multiple heat functions on at once: microwave, fan, upper heat,
  lower heat, interior lights, etc. Ex. During Speedcooking, the microwave
  and upper and/or lower lamps can be on at the same time while cooking.
• Interior light is the halogen cooking lights, so light does not stay on; cycles on/off with the cooking.
• No preheat necessary, except with convection cooking.

120 volt Advantium

• 2x-4x faster than conventional cooking
• Heat
  functions cycle one at a time: microwave, fan, upper heat, lower heat,
  lights, etc. Ex. During Speedcooking, the microwave, upper lamps and
  lower lamps cycle on at different times.
• Has a separate light for the interior light; light stays on.
• Preheating is recommended