I have a relatively expensive non-stick pan. I have a much cheaper, but very heavy, cast iron pan which is great for omelettes. It does take quite a while for the cast iron to reach the desired temperature. The non-stick pan is aluminium with a steel sheet beneath it so that it works on an induction hob.
The trick with omelettes is that the pan has to be very hot when you pour the eggs in so that they really sizzle for a couple of seconds. Then they won't stick.
The reason that ferrous pans retain their heat for such a long time, and take so long to warm up, is that iron is basically not that great a conductor of heat, compared to a lot of metals. Says he, stating the bleedin' obvious...