This is pretty much what I was thinking as I was reading. I think that a properly made grilled (or griddled) cheese sandwich is a great thing. Neither of these sandwiches sounds appealing at all.
While both don't appeal to me either, I don't see the high calorie count. Bobby's version is <300 calories for a whole grilled cheese sandwich, hardly over the top. The other guys might be a little higher but not much once you factor in the extra mayo in the recipe.
Eating a normal burger will have more calories than either of these. And if you're surprised or need a health warning that a grilled cheese sandwich has a high % of fat, well...
At the bottom of Bobby's recipe, it says
Serves 4. Per serving: 1120 calories, 68g carbs, 48g protein, 205mg cholesterol, and 73g fat
So 1 sandwich really is 1120 calories Just to make sure, I punched the ingredients into my cooking program, and adjusting for certain ingredients (for example, each slice of bread is supposed to be 1", but a normal slice of bread is about 1/2", so instead of 8 slices, I punched in 16), the full recipe really was about 5000 calories, or 1200-ish calories per serving.
Then I checked the challenger's recipe, and his says
Serves 2. Per serving: 1310 calories, 65g carbs, 59g protein, 170mg cholesterol, and 93g fat.
I allowed for a lesser amount of mayonnaise being used (4T instead of the full 9 that the mayo/balsamic combo makes), and still got roughly the same calorie count (1380) per sandwich.