When to spray or when to use olive oil?
First of all, with omelettes--any sauteed eggs really--I much prefer butter. And with omelettes, less than a teaspoon is sufficient; swirl it around the pan until fully melted, then pour off the excess. In this case, you would be using the butter for flavour, not any specific physical properties. For scrambled, user rather more. Fried eggs are generally the only time I will use olive oil, and even then I will use a mix of olive oil (for the heat) and butter (for that flavour which goes so well with eggs).

In general I prefer to avoid sprays (unless you are talking about a pump-action spray bottle which you fill yourself) as there are propellants and such used in sprays to make them work. Personally I prefer to avoid multisyllabic synthetic chemicals in my food whenever possible.

But if you must... sprays are most useful when you need a very thin but even coating of oil. Omelettes are a good example, though honestly I cannot think of another use in cookery where I would find a spray advantageous.

In baking, however, sprays can be quite useful. Especially when baking tarts, pies, or cakes which call for the pan to be buttered and then floured. A quick spray makes things much simpler.