Starks are aggressive, and in addition become even more so as they suffer casualties. Many units and generals have bonuses for units on their last ranks. They’re usually able to dish out a lot of damage, having easy access to the vulnerable condition and many tactic cards grant bonus from claiming the combat zone. They’re also highly mobile and benefit from the Manoeuvre zone a lot. If you want to manoeuvre an army that fights well, stands its ground and can go for the extra mile, the starks are great at it. They have medium cavalry that is quite versatile.
Lannisters are often seen as more defensive but I think they’re more devious stalkers, not unlike their sigil: a lion waiting in the bush. How they win is to create the right conditions for success, by being patient and then pounce for the killing blowat the right time. They usually can be given good equipment/abilities for the task, be it armor, weapons or means to undermine an opponent’s morale, but they don’t have generalist troops and most are specialized for one thing. So they’re a toolbox army, one that you can tailor on your desires. They have access to heavy cavalry, which is all about charging.
If factions have a trend in their style, generals will add a specific flair to it. Some simply emphasize the faction’s strength while others will explore a specific theme. There are also “divergeant” generals in each of those two original factions (I would guess that all factions will eventually get one). For the Starks, it’s Howland Reed, who is more of a guerilla fighter, almost akin to a Lannister, while for the Lannisters, it’s the Mountain, who is a far more violent and aggressive than usual.
I’ve done a review of the game on bgg forums if you ever wish to read more about these thoughts.
Edited format
My question is, is there some where that breaks down the various houses or factions so I can see which one might be best for my play style? As it stands it might be between Lanister and Stark if me and a buddy split a starter set but I might get the others if one suits me better. 
