Pikes and Halberds were specifically designed to make it easier to force-dismount mounted units, and halberds were also designed to offer their users some bonuses when fighting against swords in melee, hence their bonuses.
Javelins, and to a lesser degree bows, will be able to destroy shields.
I'd like to work in camels offering an initial bonus against horses, but have it be removed over time, but that would mean I have to either start tracking horses or build it into the soldier's info somehow. As for camels, I'll probably restrict them to desert, at least initially. I'm not against turning generic mount categories (horse, camel, etc.) into resources either. It'd be kind of interesting actually to have a resource that wasn't necessarily tied to a region, but required a starter stock.
Right now people tend to choose things based on what is the best. I'd like to create situations where what is "best" depends entirely on what the enemy is using. Hence pikes and halberds being able to force dismounts, ranged weapons being effective against shields, etc.