They do mean the same thing, but they have different moods. With the em-dashes it's self-interjection that foregrounds the detour, but with parentheses it's, well... parenthetical.

Aside: it's probably just style (maybe some style guides call for the way you did it), but using em-dashes for this purpose with whitespace on each side of them looks/feels wrong to me. Anyone know if that's regional or something?