Jinx-
Pros: High damage, good push, has CC, AoE crit, good chase with passive, scales amazing, great teamfight
Cons: immobile, easy to catch, close range ult is a bit inefficient because of how the damage works, can be punished early easily, summoners are only true escape (not relying on passive proc as you run away), needs a good amount of peel as well as knowledge of positioning, not alot of dueling potential
Lucian-
Pros: Lane bully, good pushing, has escape that resets, double shot passive, passive and BotRK is one of the most effective ways of dealing with tanks (BOTH shots use BotRK passive), decent scaling to mid-late game, fairly simple and safe to play, very forgiving champ overall (can make a good number of missteps and still be fine), good duelist
Cons: Doesn't scale amazingly, ult is awkward to use in certain situations, needs to know when is safe to E forward (good knowledge of positioning), teamfight isn't overwhelming (isn't bad just average)
I have probably missed things, personally I would recommend Lucian, easier to lane bully setting the enemy behind making your front line more effective as well as with Blade of the Ruined King passive % HP bonus damage being applied on BOTH shots of Lucian passive make him very effective at removing tanks from the fight.