I don't believe that a limited number of +P .38 Special rounds will do any noticeable damage to any of the steel framed J Frames. I personally practice with +P rounds only enough to be familiar with them, to know how they function, feel, and where the POI is in relation to the sight picture. I do NOT use +P rounds lighter than 135 grains. My round of choice is the Speer Gold Dot 135 grain designed for short barrels. Next in line, so close as to be pretty much a tie, is the +P lead SWCHP rounds that have been available for a lot of years and made by several manufacturers. I am comfortable that these two rounds will provide more than sufficient energy and performance to trust them for my personal defense needs.
The .357 rounds, in any loading, may provide more velocity and energy (in any revolver) than the +P .38's, but from a short barrel, a fairly large percentage of the performance of a .357 round is lost when fired from a short barrel. In addition, the additional muzzle flash, the loud, sharp report, and the additional recoil and increased recovery time is just not worth it for me. If the +P .38 Special is enough (and for me, it is more than enough), why deal with the additional negatives when firing .357 Mags? Can it be done, accurately, and effectively? Sure it can. Each of us has his or her own levels of tolerance. I can do it. I just don't see the need, and I don't find the mag loads pleasant. If I were to decide to carry them, I would feel compelled to practice with them across the board. Years of seeing police qualifications and requalifications by officers who carried .357 Mags and who only ever used .38 Special wadcutter practice ammo for those qualifications proved to me that such practice is not conducive to good shooting when your carry gun is loaded with Mags. I have seen officers who could clean their targets (the old PPC qualification targets that included 24 rounds at 50 yards) who could barely or who failed to qualify if required to do so with Mag rounds. Most of them could have done so with some practice with Mag rounds, but they could not, in most cases, have been able to score as highly with the mag rounds as compared to the wadcutters. It takes serious practice to be proficient with either round, but especially the mag rounds.
In the early days of those qualifications, +P rounds were not available. I was present when the Super Vel rounds came on the market, and they changed the picture considerably, and for the better. Today's ammo selections are much, much better than anything we had available in those days without reloading for ourselves.
So I say that you can safely fire a limited amount of +P 38 Specials, enough to be entirely familiar and proficient with them and then carry them for "on duty" purposes. But I also recommend firing at least full power standard loads in the same bullet weight for practice, as opposed to target wadcutter loads. In fact, back in the day, many of us carried double ended wadcutter rounds, poured from lead that was harder than the target wadcutter rounds were made from and reloaded tp just less than about 1000 fps, so that leading was not a serious problem with the higher velocity rounds. These were very effective personal defense loads, and we used them for duty rounds as well (before it became anathema to carry personally reloaded ammunition while on duty.
If you are familiar with your Model 60 and you shoot it well, and unless you are willing to spend the time and the serious money to become proficient with the same platform firing .357 Mag ammo, I think you should spend the money for quality +P and standard pressure .38 Special ammo and go practice. My opinion only here ... I believe you will be well prepared for serious social encounters and will likely be able to deliver those rounds to the place where they will do the most serious damage in the bargain. I'm sure others will disagree with me. I'm just telling you what I'm comfortable with after many years of carrying, using, and being present at shootings and autopsies. Today, with the good ammo available, where the bullets land is more important than the caliber used. Use what you are comfortable with and what you can most effectively use for the purpose intended!!
A model 60 with +P ammo will do anything you need to do and it still hurts to shoot it! 
