Fullmetal Alchemist. Both series start out the same, but wind up going different routes. My personal preference is for Brotherhood which stays truer to the source, but I’ve seen some people say they prefer the original.
Trigun. The original undergoes a pretty dramatic tonal shift around the halfway point, whereas the remake is more serious from the start & they seem to be aiming for a more conclusive ending (2nd season this month).
Rurouni Kenshin. Haven’t watched the original, but enjoying the remake. Continuation in the works.
Fate Zero. Prequel to Fate Stay/Night. Unlimited Blade Works is a darker, more violent take on Stay/Night.
Some newer series with similarities to JJK & CSM: Hell’s Paradise (season 2 this month), Dororo (complete), Dorohedoro (continuation in the works).