Rupture or Crash Course are the most effective physical mods to use, as they increase Vulkar's already decent Impact damage further. In combination they will grant a total of +150% Impact damage.
Heavy Caliber can be used on the Vulkar with little noticeable effect on its long-range accuracy, as its slow rate of fire ensures that its shots will always land on its crosshair. Heavy Caliber will affect the spread of additional bullets created by Split Chamber however.
When compared to the Vectis, although they have different mechanics they are essentially very similar weapons. They have the same fire rate and accuracy, and similar damage although the Vectis has 25 more total damage. The Vectis relies heavily on how fast it can reload after firing in order to maximize DPS, as increasing fire rate has less of an effect than modding for pure reload (increasing both is best, but reduces mod space). The Vulkar however has a bigger clip which makes reload time the only thing you need to mod, as the fire rate is optimal. The Vulkar also has little recoil which makes follow-up shots easier to make.