Well the courts have rules that make what parents believe in this situation moot. If the parents are both decent people, the the court will usually decide that it's in the best interest of the child for both parents to share custody, at least in the sense of legal custody. Sole custody is for situations where the other parent is completely absent or is a danger to the child. But by and large, in most families it makes sense for both parents to have a say in the big decisions that affect a child's life.
Some states don't separate out physical custody but instead refer to "custody" as covering the legal part and then "parenting time" as the physical custody side of the equation. All things being equal, both parents should have access to their child on a schedule that makes sense for the child and parents. Personally, I think that the true 50/50 splits that are popular today are hard on kids. I know many kids who do Sunday night - Wednesday night at one house, Thursday morning through Sunday night at the other, then back to the first through Monday, then the second for mid-week, back to the first for the weekend, etc. Basically 3-4 days on and off. Then other families I know do one week on, one week off. That also seems draining to me, but it seems that the kids adjust. I would be concerned that my kids wouldn't feel like either place is home, but I think that if parents can afford to do it right and really give their children their own, permanent spaces in each home, that this can work.
My husband and I have talked about splitting up and I think that if he ever were to move out, the goal would be for the kids to be here with me in our home as much as possible and for him to spend time with them here. There are many nights that I am either working or at volunteer events where it would make sense for him to come here, have dinner with them, put them to bed and then go back to his place, which would be nearby. I don't think he would be able to afford a place where he could have all 4 kids over at once and give them enough space to feel at home, so this house would still have to be the home base for much of the time with us coming in and out. Of course this would mean that we have to see each other all the time and be nice to each other and I don't imagine either one of us would date much in a situation like this ("hey don't mind my ex he'll be leaving at 10...") so that's when we say "OK might as well just stay together" and put the conversation to rest for a while.
FWIW, I have sole legal and physical custody of my oldest son because his father left before his was born and hasn't paid any child support and can't be found. We have shared legal and sole physical custody of my step-daughter because her mother abandoned her and moved out of state almost 3 years ago. Prior to that, mom had weekday custody and we had weekend visitation. My husband definitely missed out on a lot of her life back then, but logistically getting her back and forth to school an hour away every day wouldn't have made sense.
At the end of the day, there's no one answer. Every situation needs to be evaluated for what's in the best interest of the child(ren).