@Richard was on the right track, but leaves out a lot of context with the small quote. The full quote puts things in perspective:
Ziyal holds a Cardassian disruptor rifle, following
KIRA: This is a standard issue, Cardassian phase-disruptor rifle. It has a four-point-seven megajoule power capacity... three millisecond recharge and two beam settings. [...] This is a good weapon... solid and simple. You can drag it through the mud and it'll still fire.
Essentially comparing the Cardassian Standard Issue Rifle to real world AK-47, the cheap mass produced workhorse of military engagements.
Kira takes out a Federation phaser rifle.
KIRA: Now this is an entirely different animal. It's Federation standard issue. A little less powerful, but with more options... sixteen beam settings... fully autonomous recharge... multiple target acquisition... gyrostablized... the works. It's more complicated, so it's not as good a field weapon. Too many things can go wrong. [...] I think you should stick with the Cardassian rifle. It's smaller and easier to use. And if we get boarded, I don't want you to have to think too much about the weapon you're using.
The Federation standard issue rifle is a bigger, overengineered and delicate piece of equipment. Rationalizing backwards, the same can be assumed of TOS era rifles.
Then you have to account for both In-World and Production reasons. In-world, Star Fleet is a mainly Scientific and Diplomatic organization, with Defense as it's third function. It is not supposed to be a military arm.
More Specifically, The Enterprise is tasked with a diplomatic exploratory mission in deep space. The use of large fire-arms like an assault rifle would go against that mission. The use of side-arms, like a hand phaser (a self defense pistol analog), would not. We have little view of how the rest of Starfleet's standard operating procedures would differ, if any.
Production wise, Star Trek, especially in the majority of TOS episodes and TNG, is supposed to be an idealized utopian society, non-aggressive (Contrast the Mirror Universe or DS9 or Voyager, each which had different reasons to bust out the rifles more often).