There are a ton of different antennas out there, here specifically I'm talking about directional antennas.
Options include Yagi-Udas, parabolic, LDAP, etc. antennas. All of these have somewhat of a different radiation pattern and for Yagis to get the same dBi gain as parabolic ones, they need to be very very long.
Do these designs really matter? Would a Yagi with the same transmitting power and dBi gain as a parabolic one have the same range?
Would a Yagi with the same transmitting power and dBi gain as a parabolic one have the same range?
Generally, yes. As long as you keep other variables (noise, receiver sensitivity, etc...) the same.
But all these designs do indeed matter.
They are good in different use cases related to different frequency bands, the possibility of using a single antenna for more than one band, the need of low-tech antenna, wind load requirements, etc, etc...
Just to add a few more things to what fraxinus said:
Bandwidth
Yes both antennas with the same gain and power would have about the same range, but the parabolic antenna will probably have greater bandwidth. Bandwidth is a key component of communication links that cannot be ignored.
Gain
It's also only feasible to design Yagi antennas to have up to about 9dB of gain, but parabolic antennas can have much higher gains.
Frequency
Yagi antennas typically work best in frequency ranges from 3 MHz to 3 GHz. It's impractical to try to make them any bigger for lower frequencies or smaller for higher frequencies. In contrast, parabolic antennas are useful for frequencies in the GHz ranges. How many people put Yagi satellite TV antennas on their homes these days?
Size/Geometry
A yagi antenna will likely weigh very differently than a parabolic antenna with the same gain. It will also be very differently shaped which will affect how easily it can be mounted in different applications, and whether it can handle different stresses from wind and/or gravity.
