There is not. I have tested for difference and never saw much. Average MVs with identical loads from the same guns are indistinguishable.
I started using SR primers back in the late 1960s. One of my employees was a serious competitive Bullseye pistol shooter. He always used SR primers in his .38 Special reloads for his K-38.
I believe the main difference between SR and SP primers is the primer cup thickness, as SR primers are made to withstand higher pressure. There might be a problem with the use of SR primers in some revolvers if, as some do, the hammer spring has been lightened for a lighter DA pull, as the SR primers may be less sensitive. But I have never had ignition problems in using SR primers in any handgun.
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One caution. One should not attempt to use LR primers in reloading large handgun calibers. The LR primer is thicker (top to bottom) than the LP primer, and the primer will protrude above the case when fully seated. SR and SP primers are dimensionally identical, so that interchangeability problem does not exist.