Xerath probably has the best lanening, rather reliable longranged poke to spam with good waveclear, and if he lands his stun he can get alot damage in his full combo. He also has huge teamfight damage from afar, but probably the worst selfpeal amongst the 4
Ziggs tends to have less killthreat as his stuff is less reliable to land, but hios waveclear is good and if he gets to a tower, he will get plateings. Also, his aoe followup on something like a J4 ult can be rather massive and he offers more zone controll than the others.
He's also rather save vs predictable threats with his W and E, but needs to long to react to supprising all-ins.
Lux has the highest killpotential with the huge burst of her full rotation, and probably is the savest with two rather easi to land CCs and her shield. An early extra point into the shield can cockblock assasins quite badly.
Her wavecontroll needs some more effor than on the others, and her raw poke isn't as good. She's basically the sniper amongs them.
Vel is somewhere in between? His wavelcear is good, his poke is great, his full combo is about as deadly as lux, but with less range, his self peel vs targets that are already on top is bad, but he is great at keeping his distance cause his W can be cast while moveing and even Q hardly costs time with animation cancleing, his base ms is above other mages and his Q is a very spamable slow to keep people from getting close. His constant spam and the way his Q works creates supprisingly high zone controll(not as good as ziggs W+E though).
His main weakness is that he exposes him self quite a bit for waveclear or full combos, and landing his combo setup is harder than for lux or xerath, but therefor he has more dps and the truedamage to deal with high MR.