Back to iPhone after 3 years from android.

Welcome back
Must have games: depends on what you like. I'm a Strategy/Tactics/RPG person mostly. If that's your cup of tea, holler and I'll recommend.

Graphically demanding:
Wait until Brightridge HD is out. Fantastic exploration experience in its own right, I highly recommend it. Could take till next year though, he's aiming for a December submission to Apple.
XCOM with its huge sight radius in the later stages slows down a lot even on my Air1, so you could try always try that.

And Protopop (the developer) mentioned that he really cranked up the graphics for the new version. With everything set to full throttle, I expect even an Air2/6S to sweat and drop framerate. Should be more than enough to torture your new iThingie.
TA thread is here: http://forums.toucharcade.com/showthread.php?t=237171&page=74 . I pointed it to p.74 for your convenience, the screenshots are about in the middle.

Quoting Protopop from p.75:
"The HD update will be ready shortly, it looks really good on iPhone 6 and iPad Air 2, so on iPhone 6s you should be able to have it even more maxed out no problem I'm making sure to expose as many of the options as possible so you can really fine tune the visuals the way you want."

Of course, you could always try the current non-HD version. It's pretty graphics-heavy already when you crank everything up to max.

 

Always welcome, nam009
Let's see what we have...

4X Strategy games I don't have that many, and all are SciFi. I can recommend all of them:

1. Ascendancy and
2. Imperium Galactica 2: both are ports of old PC games. And released years ago, so I don't know if they are still available and/or work on iOS9.
3. Starbase Orion: really good game, and very polished.
4. Star Traders 4X Empires (Elite) : don't know what the difference between the normal and the Elite version is. Similar to Starbase Orion. Both of course reference the classic Master of Orion II.

Tactics games are all on the party/squad level, with lots of variety so you can pick what you prefer:

1. Space Hulk: the classic WH40K boardgame
2. Crowntakers: plays are short, good replay value, and fun. Fantasy.
3. Ravenmark Scourge of Estellion / Mercenaries: Scourge is a huge singleplayer campaign, Mercs is multiplayer.
4. Tactics Maiden: not the best graphics ever, but extremely well designed. Fantasy. Niebau/Mangobile made more games like this, and TM is the latest in the series. The older Kingturn series aged pretty well, though.
5. XCOM I already mentioned.
6. Warhammer Quest: Huge, but not your 99c iOS game. Worth every penny, though.
7. Battlelore Command: rather short for a Tactics game. But extremly polished, and pretty difficult. Currently on my second playthrough back-to-back.
8. Demon's Rise: Huge. Lots of stages, lots of characters. Still with the odd quirk or two, but the dev is great. Constantly working on updates and fixes. Check out the TA thread to get an impression.
9. Devils & Demons: Also fantasy. Unfortunately they didn't release the next episode yet, and it's been a long time. Still fun to play, though.
10. Swords of Anima
11. Banner Saga: refreshing and different concept. You travel with a group of people, need to manage resources on top of the fighting. Unfortunately it has quite a few problems. The worst I can remember is that if you don't build a specific character a specific way, you are pretty much screwed in the endgame. But that's what guides are for. I didn't complete it, but enjoyed it quite a lot despite its flaws.

That's about all I can think about right away in the Strategy/Tactics department, without really digging through my purchase history.

 

@Nullzone: Thanks for the recommendation for Demon's Rise. I might be a bit biased (being the developer) but I can confirm that the game is graphically intensive and should be a good test for new iOS hardware with all the graphics options enabled.

Otherwise, I'd recommend XCOM - Enemy Within. Good strategy and great graphics.