It feels like you're saying Jimmy remains more sympathetic because of his beginnings. Walt was a suburban dad saddled with cancer and couldn't have been a nicer guy. Feels like you think their arcs are polar opposites. I think they are more similar than you think.
While there are some similarities on a purely surface level regarding their arcs, they are quite different is you delve into them.
I'll explain:
On a surface level, these are two men who started off as "good guys" and broke bad out of tragedy (Cancer for Walt and losing his brother for Jimmy).
Now, let's delve deeper:
-Walt was crafted by Gilligan to be a man who was ALWAYS a monster deep down but had the beast caged via living a normal life. He was a slave to his own ego. He left Gretchen because of a sense of feeling inferior to her higher class family and it bruised his ego/sense of himself. He eventually "settled" for domestic life and grew bored of it over time. He dove into Heisenberg upon receiving his cancer diagnosis and finally felt free to let the beast out of the cage. He found his niche and a way to exercise his ego in the form of creating his meth empire. Of course, he started it as a necessity but quickly grew to love the thrill of it.
He was extended an olive branch by Elliot and Gretchen with the job offer but ultimately turned it down because he deemed their offer as "charity" and it hurt his ego. He wanted to leave his family a large sum of money after he died and wanted to be 100% responsible for it himself. In his endeavor, he became addicted to the thrill and liberation that came from being freed from his cage and it soon morphed into something more than just taking care of the family: feeding that ego of his. Being free. Being "the man", as Mike had told him.
The point here is that Walt had ALWAYS had the darkness within him and kept it repressed in life, essentially giving up on his hopes and dreams in order to settle for a normal married life. He lost his flare--his drive. The cancer gave it back--tenfold. Walt, in many ways, had a death wish. It's why he was upset about his cancer going into remission. He wanted to go out in a blaze of glory. He wanted to live free and die free.
-Jimmy is different. Yes, Jimmy always had his own darkness within him. The difference is this: Jimmy exercised it freely in his younger days. It wasn't driven by ego but rather by a sense of thrills. It was fun for him. It gave him a rush. He wasn't socially awkward like Walt and he wasn't looking to be "the best" in everything--rather, he was simply enjoying his cons and enjoyed the attention of people.
Jimmy locked his beast up, like Walt, but did so for some similar and some very different reasons:
1. He hated Chuck disapproving of him and wanted to prove he could be better.
2. He genuinely wanted to be a better man and Chuck's disappointment made him see that. This is evident when he's speaking with Marco in Season 1 and tells Marco that he, ultimately, made a change in life "for me". Chuck was the catalyst for that major life change but Jimmy wanted it not just to please Chuck but also to help himself.
This is where Walt and Jimmy fundamentally differ: Walt was driven by ego and his transition to normal suburban life was his way of giving up to a certain extent. With Jimmy it was an honest effort to make a change and be better than the darkness within him.
That's the difference--Heisenberg was a beast that was cultivated, fed and fattened up over years and years of repression, self-defeat and bruised ego. He was embittered over the Grey Matter fiasco and stewed in it for years. His pride kept him away from it.
Jimmy is different: he formulated "S'all good, man" years ago as a young man out of necessity and quickly grew to love the thrill of it (like Walt) but, later on, genuinely tried to cage that beast of his in an honest effort to do and be better. THAT is the difference between Jimmy and Walt: Jimmy tried to cage his beast and be a better man while Walt just caged his beast and made it grow out of a sense of hurt pride and self-defeat.
So, if anything, Jimmy was a criminal first, attempted to better himself, and then fell back into criminality again while Walt was a straight arrow at first and grew into a criminal over time with no desire to reform himself.
That's the difference. It IS a reversal here: Jimmy was a practicing criminal first, then tried to fly right, and fell back into it again. Walt was a law abiding man at first who grew into a criminal that was cultivated for years by his hurt pride and ego over Grey Matter as well as triggered by a cancer diagnosis.
Now for the change:
Upon receiving a cancer diagnosis, Walt was driven (at first) by desperation to leave his family money. It soon became about BOTH leaving his family money as well as making friends with his long-caged ego. He grew to love it. He admitted that at the end of the series.
Now onto Jimmy: Chuck's death is very likely Jimmy's "cancer diagnosis" but Jimmy has been strongly implied all series long (In Better Call Saul, that is) to dive into Saul Goodman out of a sense of feeling he has no other recourse--a sense of self-defeat.
This is the fundamental difference here:
Jimmy started bad, tried to be good, sunk back into bad again out of a sense of defeat / Walt started good, led a boring life as a chemistry teacher as a sense of defeat and broke bad out of necessity.
The other key difference is this:
-Jimmy is AWARE that he's doing bad things. He acknowledges it. Walt never once seemed to feel that way, nor did he ever apologize to anyone for hurting them.
I could go on and on but I think that's enough for now.