Why would the First Order be using blasters other than what they are usually assigned?
Also, I am a Stormtrooper, just of a different caliber than others. There's always a lesser leader within the Military, Captains etc, so just having a straight General without any "Commander" or such disturbs me as well.
Not to mention that the Rebels and the First Order using the same weaponry takes away from it. I personally think that First Order soldiers should use the blasters and weapons the are shown using in the movie, and that Rebels should do the same. Although, I'm not sure if you mean Rebels or Resistance, since the Rebels would've formed into the Republic some time after the Battle of Endor according to the new Canon.