Outside was cheaper for us. But we didn't go with the 'big name' outside caterers. We found a newer caterer who was willing to go above and beyond at a much more reasonable price. I also found that smaller, local restaurants provided much more reasonable catering prices.
We found outside catering to be cheaper than in house. We paid roughly $20/head but then also $4,000 for the venue for the weekend, whereas if we went with an in-house only venue it would be all together but be closer to $80-$100/head and only for the Saturday. With approx. 200 guests it was outside = $8,000+tax vs in-house = $16,000-$20,000....
Outside catering can add up your cost easily as big or small restaurants base it per person or quantity serving buffet style. Personal chefs are becoming the same though some do offer a better price per person or menu based. House seems less expensive overall since its being made fresh and a day or two ahead.
Our venue allowed outside catering but also had in house. We are paying our outside caterer almost 20 dollars more per person for about the same amount of food. We LOVE our caterer though ( my FH worked with the chef when he was in college and we wanted to support them!)