They're on roughly the same level but focus on somewhat different things. Sedgewick spends a lot of time on basic data structures like hash maps and search trees, as well as elementary algorithms like search and sorting, in great detail. Kleinberg instead approaches things more generally by tackling concepts by design technique - greedy, divide-and-conquer, dynamic, etc - and doesn't focus as much on the very basics. Kleinberg also spends a lot more time on more advanced topics like NP completeness, randomized algorithms, etc, while Sedgewick again keeps his focus on the more elementary topics.

CLRS contains pretty much everything contained in both Kleinberg and Sedgwick, so the two are essentially interchangeable in the sense that Kleinberg+CLRS contains roughly the same breadth of information as Sedgewick+CLRS. Since Sedgewick takes more time to explain the basics thoroughly, I'd say it's probably your best starting point.

Good luck!