The difference isn't just the crust; it's what you do with the eggs. A quiche is made using a custard (cooked cream/milk and eggs) while a frittata generally just uses eggs. So the texture and flavor is much different since a quiche has a creamy, custardy component that a frittata lacks -- that's what I see as the key difference much more so than the crust.
You can probably find frittata recipes that use cream, but look at the ratio of cream/milk to eggs in both recipes. In a custard, the eggs (or egg yolks) are a thickener for the cream/milk. In a frittata, the eggs are the binder for the ingredients; if it uses cream, it's just to add some richness (like in scrambled eggs). I tend to think of frittatas as being denser, or having more other ingredients in proportion to the eggs than the other ingredients in a quiche. Frittatas seem to have the consistency of scalloped potatoes, while a quiche is sort the consistency of a flan with stuff in it.
I think crustless quiches are kind of a lame idea. Diet quiche? YGBFKM. You take something loaded with eggs, cream, cheese and bacon (a quiche lorraine), and you think losing the crust will cut significant calories? That's like saying "I'll have the 24 oz porterhouse and a diet coke". Cut a smaller piece and have it with a salad, but if you're going to do it, at least do it right. If you want diet and eggs, make an egg white omelet instead.
The difference isn't vegetables either. Asparagus and gruyere quiche is a great dish in the spring. Broccoli is popular, as are onions.