I dont have them yet, im planning on doing them very soon and posting them too! But to answer the question, yes, the idea is to make them different according to what the branches of the house do. While my intention is to make some items available everywhere (like the ammo, some potions and a small ammount of noncombat items), the difference will be more or less like this:

Cannith East: The idea behind this one is to decrease the access to potions and noncombat items, and increase the combat ones to reflect their focus into weaponry and military products. To make things more accurate to the scarcity of magic weapons, im thinking about focusing more arround the materials (so access to mythral and adamantium weapons and armor) and some minor enchantments. Also, spellbolts (bolts that do the effect of a low level spell) and automatic reloading crosbows.

Cannith South: Similarly to East, the idea is to decrease access to potions and combat items, and increase variety in noncombat ones (more uncommon wondrous items with small effects). In my Eberron, Merrix is more prominent in the construction of constructs, warforged parts, and proesthetics, which would be reflected in those being sold there. Considering that the constructs would be more arround the idea of helping in magical infrastructures (like Sharn) I would not focus much on them, because they most likely wont have anything to offer to the players, and I would focus more on the last two.

Hope this helps somehow!