Start with the sun. If your backyard faces west, an open deck can be too hot to use on a July afternoon. A covered porch gives you shade and keeps you dry in a summer storm. If your yard is already shaded by trees, an open deck lets in the light you're missing.
Next, think about how you'll use it. Decks are great for grilling, sunbathing, and connecting the kitchen to the yard. Porches are better for sitting outside every evening, rain or shine, and they can be screened later to keep the mosquitoes out.
Budget matters too. A roof adds framing, roofing, and sometimes electrical work, so a covered porch usually costs more per square foot than an open deck. Many homeowners split the difference with a deck that has a smaller covered section near the door.
Whatever you build, the structure underneath is what makes it last: footings at the right depth, flashing where the ledger meets the house, and joists spaced for the boards you choose. Ask any builder to walk you through those details in the estimate.