Pro Massive galaxy to explore
Thanks to the fact that the entire galaxy of No Man's Sky is procedurally generated, the amount of planets to explore is almost endless. The number of planets would be 18,446,744,073,709,551,616. However, the fact that 2 players managed to find each other in game on the first day, seems to make this number quite questionable.
Pro Endless procedural generation
This game procedurally generates almost everything. Your spaceships are procedurally generated, so are the planets, moons, every animal on these planets, the resource nodes, trade routes, languages, etc. When discovering new species or planets, players get to rename these and leave their mark on the galaxy.
Pro Freedom to choose how you want to play
Ally with factions, trade or just be a pirate. When trading with NPC aliens, you build up a positive reputation with the faction they belong to. Alternatively you can also be hostile and attack trade ships, or even be attacked by NPC pirate spaceships. Both can be ways to get what you need, so do whatever suits your play style.
Con No clearly defined missions
The objective of the game is to ultimately reach the center of the galaxy. However, the player is completely free and unguided from the beginning. You figure it out for yourself as you start mining, crafting and upgrading your ship and gear. This game doesn't have a big story to tell.