From what I've gathered, the frittata most likely preceded the omelet. There's certainly less technique involved...you just mix it all up, pour it in a pan, and off you go. Also, omelet's are an individual item, if you have multiple guests one large frittata is easier to manage then trying to crank out 6 omelets while people are waiting.
For the one I made here the mushrooms were not added as part of the egg, but individually placed on as the egg was setting in the hot pan (like you would put a topping on a pizza). It just looks nicer that way, but it's not required at all.
Frittata tips (and eggs in general):
Use a non-stick pan with a heavy base. If you have one of the cheap thin ones, please throw it away, right now. Ok, welcome back. Now, see, a heavy base (hopefully made of a thick disc of bonded material such as copper or cast aluminum) conducts the heat so it's of even temperature. As Anthony Bourdain said, if it can't kill someone with a blow to the head, it's not heavy enough.
If you have more then one heavy non-stick pan, use the newest one. In fact, set aside your pretty new one and use it just for eggs, nothing else. Let nothing but soft plastic spatulas touch it, no scrapers or abrasives and for #%$* sake no SOS pads. This is your precious egg pan and none shall touch it but thee.
Try using 1/8th teaspoon of cream of tartar per every 2 eggs before you beat them. Trust me...it's subtle, but they really do end up being fluffier and...well, just better. Use a pinch of salt also, unsalted eggs are fairly bland.
Whip the eggs at an angle...meaning the top of each arc should come out of the egg solution and aerate the mixture. 30 seconds should be good enough, and use some energy to whip some air in there. Your eggs will be lighter and fluffier. Add the (cooked but cooled) accessories (onions, peppers, asparagus, mushrooms, potato, bits of ham or sausage...) to the egg mixture afterwards, and only very briefly stir to distribute things around.
Have your oven pre-heated and ready at 400c, top burner only (broiling).
You will use some fat in the pan, meaning butter. Margarine only in a dire emergency. "Non-stick" is a relative term, eggs will NOT just slide out of a dry non-stick pan, unless it's a faked TV commercial. It needs help with a little melted butter...besides, butter tastes awesome, hello. The pan should be medium hot, enough so the butter is frothing. Don't let it froth for long, butter burns easily and turns bitter and, well, horrible.
Just as the egg starts to set up a little, it comes off the stove and into the oven to broil a bit. The pan will already be hot when you slide it in there, you just want to finish the top of the frittata, which should at this point should still be quite liquid. Layer some cheese on there too if you like, and maybe some thinly sliced chives. Once it's solid (reach in and jiggle the pan a bit) it's done, but it's better to brown it just a little. (not too much, burned egg is nasty).
The general idea is to cook the bottom 50% on the stove, and the top 50% in the oven. Slice it up like a pie and serve with the usual bacon and fried potatoes. Now have some coffee and soak in the compliments. You rule.
There are many recipes out there, but hopefully this technique stuff is helpful, also.