An iOS strategy game on the level of Outwitters? Good luck with that. Here are some well-designed strategy games on iOS, but these all have a higher degree of luck than Outwitters. That doesn't mean they aren't fun, but it hurts the development of a large competitive community.
Ascension: A non-TCG card game with no microtransactions. Basically instead of building a deck before the game, you and your opponent build a deck as the game progresses by choosing cards from the center. As the game goes on you use your cards to acquire better cards and try to balance your decks while scoring points. It's a nice change of pace from TCGs.
Ravenmark: There are two games in this series. One is a singleplayer campaign, one is a multiplayer game. In this game you control small groups of units and try to outmaneuver your opponent on a battlefield. Placing units together into formations will make them stronger, but far less mobile and prone to being flanked or being harassed by ranged units. Ultimately it wasn't for me, but it's certainly an interesting game worth checking out for all TBS fans.
Autumn Dynasty: Amazingly well done RTS for the iOS interface. It has a singleplayer campaign, AI skirmishes, and real player skirmishes. If you're a fan of RTS games you can't really go wrong here. The controls work brilliantly. The game has simple mechanics which make it easy to dive into, but also has plenty of room for more complex strategies (kind of like Outwitters). I highly recommend this game EXCEPT, the sequel Autumn Dynasty Warlords is coming out in 1-2 weeks so you might want to hold off and get that instead.
Also I recommend checking out %url% if you're interested in strategy games on iOS.
That's all I can really think of for now, but I'd like to add one more thing. You can quote me, "there will never be a strategy game on iOS that is as good as or better than Outwitters in terms of pure, strategic depth." iOS will die off before anyone can top Outwitters, perhaps even if OML makes an Outwitters 2. I'm not saying there can't be other fun iOS strategy games, but they'll likely incorporate more luck and/or be unnecessarily complicated for pure (as in simple basic mechanics like chess), competitive potential compared to Outwitters. Think of other well-received TBS like Fire Emblem. It can certainly be a fun game and we'll probably see good TBS like that, but it's in a different vein from Outwitters and can't hold a candlestick up to it when it comes to 1v1. Or, take some well designed card games like Ascension. It's certainly competitive and takes skill, but there is also quite a lot of luck. These games are all good, but if you're looking for a true test of your skill I don't think you'll find anything better than Outwitters on the appstore.
Starcraft 2 is the only strategy game I really play regularly besides Outwitters. For other games outside of iOS you could check out Infinity Wars. I don't really have the time for it but if you like TCGs it actually brings some cool new mechanics to the table and is probably worth looking into. I don't think it's too hard to get a beta key from people on their forums. Of course, there is also Planetary Annihilation but I'm sure most of you have heard of that. If not, it's basically an RTS where you can travel between multiple planets, asteroids, and/or moons during the course of a single game. You can even do things like alter the trajectory of an asteroid so that it collides with a planet. It's in beta at the moment so I can't really recommend anyone get it but it might be worth keeping an eye on if you're into RTS (especially if you enjoy games like Total Annihilation).