I started with Spartan strike, but only because I've already seen plenty of vids of Spartan Assault.
The controls work fine once you get used to it. The main problem is that virtual control "sticks" don't have a physical limit to how far you can move it, so sometimes you will find your fingers going off the edge of screen in the heat of combat.
However, I eventually got used to not needing to move the controls so much. Each mission gives you default abilities and weapons, which you upgrade with in-game credit. You earn credits from winning missions. The currency is purely an in-game thing, not freemium BS. Credits will be needed to use the UNSC heavy weapons like the sniper rifle, spartan laser, or rocket launcher. Everything is done before the mission starts, so no in-game menus. Definitely arcade style.
Overall, I'm fairly impressed. EVERYTHING from the full Halo games are there. All the vehicles, abilities and weapons are in there, and you can pick dropped enemy weapons as well. The sound effects are authentic. It's literally a top-down view full featured HALO game on your iDevice.