Mouseover when on the ground shows damage neither modified by weapon power nor by +damage%.
Mouseover in ship screen when in space shows damage modified for ... not even a clue ...
Mouseover in action bar when in space shows damage modified for weapon power and +%damage.
That's the big difference.
And not technically a bug, just ... very annoying.

Basic rule: if you want to see what a piece of ship equipment does, check in system space.

For a decently spec'ed character, with Borg Console and no further specials, ignoring accuracy-to-crit conversion (which would increase the value of CrtH, CrtD and Acc even further), the different weapon mods calculate to these increases:

[Acc] if not hitting 100%: >>>>>> ALL
[CrtH]: ~1.55%
[Dmg]: ~1.45%
[Acc]: ~1.35% (needs to be confirmed, based on theoretical conversion values)
[CrtD]: ~1%

CrtD, CrtH and even ACC scale with each other multiplicative though, so with multiple mods CrtH gains a bigger lead, CrtD catches up quickly, and so does Acc probably. DPS-wise, the perfect weapon would be [CrtH]x2 [CrtD], or [CrtH]x3 for Antiproton.

Not that [Dmg] is really far behind, it isn't - but it is technically the worst mod. It's really close though.