Deck.
The style of this one is more refined, with the thick benches, trim piece around the edge of the deck, and even the angled boards along the outside of the steps. This one appears to be cedar and the other is just regular treated lumber. Cedar is pricey and cost prohibitive, however, you can stain the deck or use stuff similar to what we used on grandma's (it comes in lots of colors) which not only protects it but also minimizes splitters.
Something to keep in mind is that your door is very high off the ground. It WILL have to have a railing around it because of it's height. That being said, you can use something like this near the door - maybe an 8x10 area (I'm just throwing out a number) with the long steps on one side then put rails on the other two sides. You can incorporate benches with backs into those.
Pretty awesome. Just remember that you'll need a rail on the two sides that won't have steps and reality says (and code) that you need a handrail on at least one side of the steps since you'll be so high. You could (depending on how much work your grandpa is willing to do) do this same look on the east and west sides with the protective railing on the south side and handrails down one side of each wing of the steps.
Really think about the size. We want to be conscious of budget but you also want a deck that functions for what you want it to do. Will you have a grill on it, and if so, what size (now or later)? Do you want people to hang out on the deck, if so, how many? Do you want room for chairs or lounges? Do you want access to the yard, if so, from which side? Do you want privacy, if so, what side, and how much?
Closing it in underneath is a nice option because you don't have to worry about weeds and such. That being said, you would have enough height that gravel could be put down and you could put a door (even a lock) on it for storage.
Q