Power doesn't have anything to do with speed, power helps range. Omni antenna radiation patterns look like a big ass doughnut. The higher db the antenna is rated, the flatter the pattern is, which translates in farther range, but with the loss of some signal above or below the horizon of the antenna.
Also transmitter output is measured in watts, not dbi.
Here's an example...
The HakShop USB RT8187L WiFi Adapter, outputs at 1000mW, with a 5dBi antenna for a combined 35db of power.
If you were to replace the antenna with a 3dBi (awesome for wardriving in cities with multistory buildings) you'd have 33db of power, so less range, but the radiation pattern would be more spherical.
Now if you were to go crazy and stick a 15dBi antenna you'd up the power to 45db, with a really flat radiation pattern.