if you have the artifact relic, you retain your 3 strength from the relic, so that's probably objectively better than jax in all cases
some classes (silent, watcher) benefit from strength a lot more than others (ironclad, defect). watcher's damage is essentially doubled/tripled in wrath/divinity per point of strength and silent loves those shivs, not to mention other multi hit cards like riddle with holes.
being able to remove 2 strikes can often be more valuable than what you get. even if you get, say, compile driver and leap, that's a nice improvement to your deck.
I struggle with cards that damage you in classes where you don't have a way to heal, so I'm often scared of taking jax. but it's a great way to scale in fights where you might need it.