Normally, a manufacturer will post 2 types of plots. For an omnidirectional antenna that's typically mounted straight up on a vertical mast, the Horizontal pattern (not surprisingly) resembles a full circle. I find that in the higher frequency bands, the Horizontal pattern is also called the Azimuth, because if you are using a directional or yagi antenna, the Azimuth pattern would tell you the direction where most of your antenna pattern is focused.
The more telling pattern (in regards to your question) will be the vertical pattern or elevation plot. This would be the "side view" of the antenna pattern, and would show the main beam, as well as any lobes or downtilt that is built into the antenna. From the way you asked your question, I think you already realize that the horizontal pattern will become more compressed as the antenna gain is increased. We often use the analogy that a Unity gain (zero gain) antenna resembles a real fat bagel, while a high gain antenna pattern becomes flattened down like a pancake. You've still go the same amount of dough, just the shape has changed. It's important to realize that the total energy being transmitted has not changed, you have only changed the pattern. Getting a "gain" in one area means that energy is no longer present somewhere else.
As others have said, any decent manufacturer will have charts and plot patterns for any antenna they're making, and you can compare them to see the differences.
If you haven't seen it before - this guy Nigel has a pretty good Blog that's focused on WiFi - but he's not US Based, so some of his observations don't have a US perspective as far as what's legal or common.
WifiNigel: Antenna Radiation Patterns in the Real World