CastleBravo: Is it possible you failed to consider the alternative?
I bought my .357 conversion barrel so that I might have the option to shoot in that caliber, not because .40 doesn't do it for me. It wasn't about improving my groups. It was about having "two guns in one".
One advantage that comes to mind is this: I recently went to my favorite gun store to buy some ammo. As luck would have it, they were out of .40 and were not expecting a new consignment of the wildly popular cartridge for several days; but they had plenty of .357 SIG in stock. I didn't have to wait to go to the range.
Another one is this: In a global SHTF scenario (not that I expect one to happen any time soon) most gunners will find themselves up a creek, what with 9mm/.40/.45 caliber shortages and all. The only one you might come by in any number, if at all, is the .357 SIG.
So you see, having equally tight groups only confirms that it was money well spent. Not the other way around.