Something I was meaning to point out earlier is that DCEU Superman appears to be a lot more powerful than Arrowverse Superman (based on his power feats in MoS, B v S and JL - particularly JL) .
I feel like DCEU Superman would crush Arrowverse Superman pretty easily. Even if Supergirl were as powerful as Arrowverse Superman, I feel like DCEU WW would still take her down - given that she takes a headbutt from DCEU Supes without serious injury (and she's not actually trying to harm him ), she also stood her ground against Doomsday and Steppenwolf.
Kara isn't even remotely as tough as those opponents - I can't see her being that much of a challenge for WW.
As for her DEO training - well WW trained since she could walk with the greatest fighters in history, some sparring with Alex at the DEO doesn't even begin to come close.
Again, Supergirl is probably stronger, faster and has a higher resistance to injury, but WW can clearly fight stronger, faster and tougher opponents (e.g. Doomsday, Steppenwolf ) and do very well.
Given the enormous disparity in fighting skills between Diana and Kara, (and Diana's speed, as shown in JL) I can't see Kara winning. In a hand-to-hand (no weapons) fight, Kara might last a while, but in a fight where WW has her weapons, it would be over in very short order.
I think we'll just have to agree to disagree, on this one.