If what's there is stable, you could pour new slabs on top of it,
which would also be easy. For a really nice look, consider stamped
concrete, though this is not something you can do yourself. Stamped
concrete can be done to look like slate, cobble stone, brick, etc.
Another choice is pavers.
If you go with the decking idea, I'd look at the Trek type materials
that are composite. They cost more, but no maintenance is required.
An advantage to decking is that it doesn't require a stable base over
the entire old area. You can support the new deck with footings,
though that means the new deck will be considerably higher.
One key to all this is how much room you have for a change in grade,
as any of these solutions will require a minimum of several inchs in