Eq imperatoris are better early on, but caesaris excel later in the server, when atk per hour is the main factor. When you train troops everywhere 24/7, and you either have enough EI to keep raiding or stopped raiding altogether, EC become more interesting.
If you swap the horses you're making mid round you will be giving up some of the power you would get from the hero weapon. Haven't done the maths, but you will probably need to splat your army or make a LOT of ECs to make up for the weapon swap after starting out with EIs.