Generally and technically, the difference is "first gaussian blur, then median filter" (mode 1) -vs.- "fist median filter, then gaussian blur" (mode 2). Due to the either-or nature of median, it changes the behaviour on certain pixel constellations (i.e. extremely fine/thin detail, or e.g. DCT artifacts).
On most sources, the differences between mode 1 and 2 are pretty minute. If you don't see a difference, then it doesn't matter. That simple.
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There is no hard rule when artifacts start to appear. (Speaking
strictly, artifacts are introduced already at the weakest notch.)
Keep in mind that the
apparent strength of sharpening, as well as introduction of artifacts, also depend strongly on the "cstr" value. If you want to get more "BOOM" into the picture, you should rather reduce cstr, instead of raising sstr by too much. Also, switching the cstr operation from gaussian-kernel (positive sstr) to box-kernel (negative sstr) can make some gentle difference.