The biggest difference is the beam arcs: there is a greater overlap as they are focused more towards the fore on the Apollo. This means you will have both beams firing at targets in front of you over a wider area, rather than the narrower overlap we currently have on the Artemis class cruiser. Instead of having a 90′ forward angle where both beams fire, you now have a wider angle of about 120′. You can therefore engage more targets with both primary beams more quickly as you will have to manoeuvre less to bring them both to bear. I think this will make quite a big difference to the damage the ship causes.
In terms of the cycle time; over a longer engagement with beams, you should be able to fire a greater number of primary beam volleys due to the cycle time. Something like, for every 5 shots the Artemis fires, the Apollo fires 6.