Some anime that I really enjoyed,
1) Akame Ga Kill
2)Naruto/Shippuden (dont mind the fillers, they explain all the character traits)
3) Aldnoah Zero
5) Case Closed (periodically when Im in the mood for a detective)
6) FATE/ZERO ( I must have watched Gilgamesh vs Rider 1000 times. )
Some non-anime movies I like
2) Tears of the Sun
3) King Alexander
5) Ip Man 1/2/3/
6) Anything Marvel or DC
I enjoy mostly anime that have a "imperial" feel to it. Like a chain of command. Also with a hint of god like influence or a mythical story line based on some interpretation of a real life myth.
I won't ever read the Naruto Manga! All anime for me!
If you haven't already go watch FATE/UBW (The new one), I personally preferred it over ZERO.
Besides that obvious one (That you've probably watched already), here are a few action/sifi/horror shows that you might like;
1. Parasyte - the maxim (Gorey and action packed, one of my favs)
2. Mirai Nikki (Action and Sifi w/ a bit of romance)
3. Elfen Lied (Lots of action and gore; there is nudity just so you know)
4. Deadman Wonderland (Good action show, just incomplete. Manga is good however)
5. Psycho Pass (Good action and story)
6. Higurashi : When they cry (Good story driven show, lots of children killing each other )
7. Gurren Lagann (Must watch for anyone into anime imo)
8. Monogatari series (Ton of stuff here; I wouldn't call it purely action, but it has it's fair share)
9. Puella Magi Madoka Magica (Took me a while to get into but the ending is very good imo)
10. Re:ZERO (Currently airing, very popular. I'm personally like it, but might not be your type of thing)
I've got a TON more since I'm not to into the whole action genre myself, so if you have questions feel free to reply and ask for more
Heroic Legend of Arslan. Big epic battles. Intrigue. Ancient/medieval look, which you seem to like from your movies.
K. Plot. Mystery. Great characters. Also good fight scenes. Modern urban setting.