I carry a 38 on duty, loaded with Federal Nyclad +P's, but only because I'm limited to 38's. If it were up to me, I'd carry a good magnum load. My house gun is also loaded with 38 +P's, but that's mostly because my fiancee is there alone two nights a week, and I don't think she'd handle the magnums as well. If I lived alone it would be different. The recoil equation is up to you, the 357 bucks and roars a lot more, but it's also a better stopper than ANY 38 load, plus P or not.
I was also a police firearms instructor, and while we practiced with 38's, we carried magnum rounds on duty. It was cheaper, it was easier on the guns, and we figured in those naive days that the guys would never notice the difference in the stress of a shooting situation. Luckily, we never found out in the time I was there, the only shots fired were at animals. The biggest advantage of the 357 is the amount of hydrostatic shock it imparts in liquid targets, something the 38 can't approach. People hit in the thorax with 357's tend to go down RIGHT NOW, as opposed to bad guys who soaked up several 38's before giving up. Faster is better. There wouldn't be so much emphasis on energy figures if they didn't mean anything!
Papajohn
