Is the Uncharted series really based on Tomb Raider?

Somewhat, yes, uncharted lifted the general layout and approach of Tomb Raider, but they don't feature the puzzles as Tomb Raider does. Uncharted games are a lot more like Gears of War. Uncharted seems to have influenced the new Tomb Raider games.

Also, Tomb Raider doesn't quite possess the same cinematic approach that Uncharted delivers. However, both games employ a lot of quality characters and combat between villains and heroes. Uncharted is more like an epic adventure that keeps you on the edge of your seat. It appears, in a sense, that both games have influenced one another.