The construction/remodel gurus can correct me if I’m wrong but to some extent it depends on where you are in the pricing cycle. When home prices are expensive, it almost always makes more sense to add on because you already own the land, so you don’t have to pay for it twice. You’re just paying for the materials and labor for the addition. So you enjoy what’s called “forced value” in your home. That is, your addition might cost you $150/square foot but the “value” might be $350/square foot after it’s completed.
But when home prices are really cheap it might make more sense to buy a whole new house.
My guess is that, more often than not, adding an addition is cheaper and more financially beneficial than buying a whole new house (assuming your contractor isn’t a clown that’s trying to rip you off). But, again, I think it depends on where the market is for resale homes versus the cost of doing the addition.
I recently did an addition to my place for about $125/square foot. Even though my place is overvalued right now, I doubt it will fall to below $125/square foot. If it does, I’ll probably be in a below-ground bunker hording food.