Be careful if you are using SuperShuttle on a shared-car basis. They don't just take tourist visitors from LAX; they also take locals too. Whilst the locals are lovely people, some of the areas they are dropped off at can feel a little unsafe.
Whereas with Karmel, they only (as far as I know) take tourist visitors, have genuinely decent staff drivers who provide a good welcome to LA and Anaheim.
Yes, with Karmel you have to call them when you arrive but this can be done from the payphones at the arrivals area in LAX, without too many difficulties. Waiting is dependent on traffic conditions within the airport as a whole, but overall they don't keep you waiting that long.