Discovery is meant to be a science ship, but I get the feeling the show regards it as being just as powerful as any other class, because we see it coming to the aid of a Shepard class, and it engages the Klingon extremist's flagship, which would probably be less advisable for a pure research platform to do.
Well, isn't that more a function of being able to get to those fights than being able to fight them? The hero ship is the only one fast enough to come and help the bushed Gagarin - but tellingly, she loses that fight, apparently only managing to menace a small BoP out of all the Klingon types involved.
The Klingon "flagship" in turn came for the heroes. But a lumbering flying cemetery apparently isn't the most fearsome combat opponent imaginable. Especially if unshielded, lurking behind the false security of a cloak.
I say, let the heroes keep on winning that way, using their smarts (if not always technobabble). Given the frugal VFX so far, it may be we won't see much pew-pew from competing Starfleet ships after all, allowing us to believe in their greater firepower with accompanying beefier looks of death rays.
I hope the VFX folks show more hero ship combat action up close, though, up to and including finally deciding where all those torpedoes are coming from...
The way I've recently chosen to think of alternative weapons, such as laser, ballistic weapons, etc, is that perhaps Starfleet maintains some alternative armories for specialist situations. Maybe weapons lockers onboard a Constitution-class vessel of this time contain something like 10 hand phasers, 10 phaser rifles, a photon-rocket launcher, a photon-grenade launcher, 2 laser pistols, a ballistic weapon, with each used for specialist situations.
...Perhaps this is why the sidearms of the day have three barrels to choose from? A laser barrel makes itself useful when there are alien elevator doors or other armor to be pierced, even if it doesn't shine in combat. The phaser barrel, vice versa.
Phasers eventually come to be seen as the most versatile, as they are the only ones with a stun setting.
Or then the separate stun device, a descendant of the MACO stun batons, is integrated into whatever weapon type is otherwise favored. Hence the third barrel in DSC/"The Cage"... (Or the second one in Kelvin.)
Timo Saloniemi