Toaru Majutsu no Index, Fate/stay night: Unlimited Blade Works Recommendations
Both Main Characthers have a strong desire to do what is morally right and will try to save as many people as possible, even if they have to risk their own lives to do it.
Both have very similar action and atmosphere. Character tropes are also very identical:
Toosaka Rin - Misaka Mikoto
Emiya Shirou - Kamijou Touma
Saber - Index
Gilgamesh - Accelerator