My hope is that the Alexander family gets whatever outcome causes them the least pain. Nothing can fix what Jodi destroyed, but the immediate sense of loss and horror can fade.
I don't think that a death sentence for Jodi will accomplish that for them. Giving Jodi a dozen opportunities to appeal will mean that claims of abuse and pedophilia will be heard over and over again. The details of the murder will be debated endlessly, and the finding of cruelty will rely on describing in detail the sequence of injuries and how much pain and terror Travis felt. I am dreading what that family will have to endure today, and I wouldn't want it to be something that they ever have to do again.
I also think Jodi would find a way to become the poster child for some opponents of capital punishment. Just as ALV did, they'll allow themselves to believe enough of Jodi's lies to justify their support of her cause. Perhaps "believe" isn't the right word, since I don't think ALV actually believed Jodi. The mindset will be that she can be presented as a victim as long as you can find experts who will swear that there was abuse and the subsequent meltdown wasn't really her fault. To that extent, she'll be a justifiable means to an end.
Contrast that with LWOP. She'll probably have one procedural appeal where they'll look at what evidence was admitted and how the jury was instructed and rule on whether Jodi received a fair trial. That's it. She might get another appeal on speedy trial grounds, even though the long delay between arrest and trial was approved by her every step of the way. After that there are no reasonable grounds for more legal shenanigans and she'll fade into obscurity or become a punch line for every comedian who makes a joke about a bad celebrity breakup.
Sadly, this crime was extraordinarily cruel and I think Jodi will be sentenced to death. After that the circus will continue. Jodi will enjoy being the center of attention, fancying herself to be the Ringmaster, even though she's just another sideshow for the Anti-DP cause. She'll embellish her story and will eventually find a way to "remember" an account of the stabbing that makes it sound like she was fighting for her life the whole time. Humbug.