Both a deck and a patio add good resale value to homes and increase your homes value.
But usually a deck that is covered and nicely made and looks nice adds a lot more value to your home and increases it's resale value much more.
If I were looking to buy another home I would pay more money for a home with a nice wooden deck that is covered than one with just an uncovered patio.
Decks are really nice to sit outside on even when it's raining and have dinner outside with family.
I had a deck built onto my house that is large enough for the whole family to spend time outside on and it's really nice to sit out there on the deck and even watch the kids play outside in the yard.
Patios are also nice but having a deck is much better than a standard patio as long as the deck is nicely done.
If the deck isn't made nice enough then it won't add much if any resale value to the home but a nice done professionally made and designed deck will add thousands of dollars to the resale value of the home.