Basic is still pretty basic.. but there are some tactical moves... (I've read it but not had time to play out a combat yet so actual play may vary some...

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Now, weapon choice during a combat can matter and isn't just on the "build" side, as you might switch party way through. Also, there is a "hold at bay" option where if you have a longer reach you can keep your opponent from getting withing striking range of you. They can attack the weapon to knock it aside and move in, but it does slow them down some. Very handy for a Mage who uses a quarterstaff (with a 7 or 8' reach IIRC).
Also, your defense die changes depending on how many opponents are there and where they are positioned... you only get your D20 for your front 3 opponents... and if someone gets behind you, you only get a D8 to defend... and you'd better hope it's not the thief.
What I also feel helps it seem a bit more "tactical" is that with the count-up initiative system, you can change your actions and "reset" your clock to react as things change... so if you're charging in and someone sets a spear, you can decide if you want to slow down... continue... try and change direction... if you're moving into attack and suddenly see a spell caster starting to cast, you can change direction to move for cover, etc. Also, doing actions to deter an intelligent opponent can also be useful. Nothing like having an archer draw his bow so that the enemy cower behind their sheilds for cover so that your battle axe wielding dwarf (who's not so fast on his feet) can get in a bit closer to the attack...
As others have mentioned though, there are a lot more options planned for AHM which I'm sure will spice it up even more (like detail crit tables).