What's the advantage of a cigarette pack -sized mobile phone over a not-exactly-huge pocket calculator -sized one? Beats me, and the disadvantages are legion, but people still buy those.
Type 1 was a "civilian" weapon in "Devil in the Dark", not a concealed carry one. We might assume it has been sized and shaped to be comfortably carried 24/7 without needing a special holster or belt, because civilians would complain about the angularity and extra weight of Type 2. Also, our heroes might well more or less permanently carry a Type 1, unless special circumstances dictated otherwise. When were they ever caught unarmed? It's more a case of them sometimes leaving Type 1 behind (or inserting it in its usual place) when packing a Type 2, and then being deprived of that due to a plot twist.