Crest12
Okay, so just by looking at your ships in game, (haven't tested them yet), I've noticed some things.
NOTE: I'm not one of the teachers here, so take my advice with a grain of salt!
On your second design, the Elyta, I noticed that you had A LOT of reactors. Probably too many, to be honest. For instance, the four reactors on the heavy laser batteries seems quite excessive, and ESPECIALLY the three reactors for the flak batteries. One reactor can power two shields fairly comfortably from my experience (if they are placed close together, which is something you should consider), and the factories that produce ammo need very little power. This also goes for the cannon batteries - I think you have too many reactors, and they are spaced quite far away. I'd also remove the backwards facing cannons myself and replace them with thrusters, as your ship seems like it'd be rather slow, and the rear cannons will seldom see action.
In general, on both designs, you have a lot of factories, and a lot of extra crew. You don't need 5 factories for 3 large cannons. If you find that the cannons are firing too slowly, move your crew and reactors closer to them. As for crew, you probably don't need nearly that many.
Your first design seems a better than the second, with better internal arrangement. Still, it could use more thrusters, and could still cut down on crew/factories for sure.
I'll edit this post with battle/test results later.
Good luck!
EDIT: Your ships were surprisingly robust! I tested your two ships against my Reaper ship variants (no piloting, only A.I.) and was only able to win against your Elyta using one of my ships (the small cannon version with no flak, posted below)
Though it is important to note: the Reaper has been specifically designed not to exceed 1 million credits, and both of your designs were more expensive, so that greatly affects things. I don't have any well designed ships in the 1-2 million range to use for testing.
I'll have to do more testing tomorrow, and see what modifications I can make to my own ships (while remaining under 1 million credits), as well as see what other advice I can offer (though by then, hopefully the more experienced folks around here will have given you pointers).