Both give you somewhere flat to sit outside, and the right answer depends on your ground, your aspect and how much maintenance you are honestly prepared to do. Paving lasts longer and asks less of you. Decking is cheaper to build over uneven or sloping ground and feels warmer underfoot.
Cost
On level ground a patio and a deck of the same size often come out surprisingly close, because paving needs excavation and a sub-base while decking needs a frame. On sloping ground decking pulls clearly ahead, because a deck can be levelled on posts instead of building up retaining walls.
Maintenance and lifespan
Good paving, laid on a proper base, will look after itself for decades with an occasional wash. Timber decking needs cleaning and treating and will typically want replacing or substantially repairing after ten to fifteen years. Composite decking lasts longer than timber and costs more up front.
Aspect and safety
A shaded, north-facing deck grows algae and gets slippery. Paving in the same spot copes far better. In full sun, decking stays comfortable underfoot where dark paving can get hot.
- Sloping garden: decking usually wins
- Shaded or damp garden: paving usually wins
- Level, sunny garden: either, choose on looks and budget
- Directly outside a back door: paving is easier to get level with the threshold
The part that decides longevity
Whichever you choose, the ground preparation is what makes it last. A patio laid without a proper sub-base will sink and rock. A deck built without adequate joist support and ventilation will sag and rot early. That preparation is not the visible part of the job, but it is what you are really paying for.