But even the heaviest cavalry will suffer appalling losses charging against spears (a welcome change from vanilla, where I found even the heaviest spearmen would be wiped out by a cavalry charge), and cavalry really cannot melee at all - they are for charging only. So, sword or axe infantry will be utterly annihilated by a cavalry charge, but will carve through a unit of spears in short order. The thing I like about BC is that the distinctions between the unit classes seem much more stark.
In my experience Broken Crescent seems pretty good. Or you might try downloading a mod, some have campaign AI which lets the other factions develop better. The only thing I find helps is to help the AI in its development more directly by giving it free buildings and large cities I don't know any way of doing this besides modding. Though, don't expect either option to work very well the AI is useless at managing its money so usually it will simply squander any extra income on more huge stacks of town militia and ballistae to march around its empire doing nothing. This is a fixed amount of income that each faction gets every turn, so increasing the entry will make the Turks richer. Assuming your game is set up for modding, you need to open descr_strat (I think), scroll down to the Turks section and then change the "king's purse" entry.
If on the other hand you want to permanently increase a given faction's income, you need to do some modding. Then type add_money turks 20000, say, to give the Turks a one-off boost of 20000 florins. To give the Turks a one-time sum of money you need to open the console using the ' key (the exact key varies, try different keys until you find it).