In addition to the two you mentioned, here are my current favs...
Neuroshima Hex: You can play against the AI or online.
Summoner Wars: Like NH, you can play the AI or play online (once you've bought some IAP).
Magic: Very deep single-player campaign once you unlock the game ($9.99). The online is turn-based, but not asynchronous (meaning you must both be available to play at the same time, and can't just make a move whenever you want).
Ascension: Easier to pick up than Magic. Can't remember if you have to purchase anything to play online or not. Both single player and online are great.
Dice with Buddies: Yahtzee-like game. You can only play online. There is no single-player mode. The thing I like about this game that I wish all asynchronous games would add is a complete list of your wins, loses, and forfeits, along with the number of games you've played and your winning percentage. You can also view other user's records as well.
A few that I haven't tried but have heard good things about...
Ticket to Ride Pocket: The iPhone version has online multiplayer and has "Pocket" on the end of its name. The iPad version does not have online multiplayer.
Dominion: Not an official port, but created with permission of parent company.
Current Favs: Summoner Wars, Carcassonne, Ascension, Ticket to Ride, Neuroshima Hex, W.E.L.D.E.R.
- Uniwar HD: A game that has stood the test of AppStore for quite some time now and is a solid tbs game with full asynchronous multiplayer and map editor.
- Battle for Wesnoth: Think larger maps, a ton more scenarios, a ton more upgradable classes. A classic (I feel) must have for tbs fans.
- Starbase Orion: A game I could never part with. You'll get the freedom of just about total customization in all aspects of the game and asynchronous multiplayer. The Devs support making this gem better to the fullest. Strong community of players like Uniwar.
As said in prior posts:
- Neuroshima Hex.
- Magic 2013.
Solid choices but they're a bit more technical and maybe outside of what your looking for, but still IMO must haves as tbs games.