I think all three are effectively the same, i.e. 128 bit bitwise operations. The reason different forms exist is probably historical, but I'm not certain. I guess it's possible that there may be some additional behaviour in the floating point versions, e.g. when there are NaNs, but this is pure guesswork. For normal inputs the instructions seem to be interchangeable, e.g.
#include <stdio.h>
#include <emmintrin.h>
#include <pmmintrin.h>
#include <xmmintrin.h>
int main(void)
{
__m128i a = _mm_set1_epi32(1);
__m128i b = _mm_set1_epi32(2);
__m128i c = _mm_or_si128(a, b);
__m128 x = _mm_set1_ps(1.25f);
__m128 y = _mm_set1_ps(1.5f);
__m128 z = _mm_or_ps(x, y);
printf("a = %vld, b = %vld, c = %vld\n", a, b, c);
printf("x = %vf, y = %vf, z = %vf\n", x, y, z);
c = (__m128i)_mm_or_ps((__m128)a, (__m128)b);
z = (__m128)_mm_or_si128((__m128i)x, (__m128i)y);
printf("a = %vld, b = %vld, c = %vld\n", a, b, c);
printf("x = %vf, y = %vf, z = %vf\n", x, y, z);
return 0;
}
$ gcc -Wall -msse3 por.c -o por
$ ./por
a = 1 1 1 1, b = 2 2 2 2, c = 3 3 3 3
x = 1.250000 1.250000 1.250000 1.250000, y = 1.500000 1.500000 1.500000 1.500000, z = 1.750000 1.750000 1.750000 1.750000
a = 1 1 1 1, b = 2 2 2 2, c = 3 3 3 3
x = 1.250000 1.250000 1.250000 1.250000, y = 1.500000 1.500000 1.500000 1.500000, z = 1.750000 1.750000 1.750000 1.750000