I may be wrong, but I believe that all the difficulty settings pertain to the battle maps, not the strategic map. The only exception is that on the easier settings you get a little more money to start with. (At least this is the understanding I took from the manual and from section 1.3 of the "begginers guide" that is stickied in the guides section.) I also don't think there is a way to change the difficulty settings after you have started a campaign.

If battles with two bridges are too easy then try to restrain yourself from using the second bridge - slug it out instead, or use a lot of missiles to break the enemy from across the river. Still a lot of fun. I've seen the AI use the second bridge - if it has the troops it will try to flank, or will at least send some mounted missiles and a spear over to defend it. I've tried lots of different things at bridges - when attacking I always enjoy throwing some heavy melee infantry onto the bridge to hack away while I cycle units of javelins in behind them - bloody, bloody, bloody. I've lost bridge battles two ways: (1) I got into an attritive slugfest but didn't have enough troops to outlast my opponent, and (2) I broke his frontline forces and charged across the bridge pell-mell, only to see him rally and swarm my disorganized pursuers, trapping my commander leading to a general route.