"Eating out is much more expensive than eating at home" is correct to say that it's cheaper to eat in your house than it is to eat at a restaurant. "Eating out is much more expensive at home" only has meaning if you are say for example on holiday somewhere. If I am in Paris but I live in London I could say "Eating out is more expensive at home" and mean that it's cheaper to eat out in Paris than it is when I'm at home in London if that make sense.