There are many YouTune videos about this already. From what I gathered, the antenna range will depend on the topography of your area. If you live in a city with a lot of tall buildings or hills a lower dBi antenna would probably be best. If you live in an area that is mainly flat and no tall buildings or hills, a higher dBi antenna would probably be best. This will also depend on the amount of HNT miners in your area.
I live in an area that is mainly flat and not tall building. The next HNT miner is about 25 miles from me. So, I bought on Nebra Outdoor miner, and two RAK indoor miners. The Nebra antenna is a 3 dBi antenna with a range of upto 10 miles in optimal conditions. The Nebra miner will be on my roof, and the indoor miners will be at my families homes. I’m hoping the Nebra will be able to see the RAK miners, from a few miles away with the stock antenna. If not, I will buy a 5 dBi antenna for the Nebra.
The Bobcat miner comes with a 4 dBi antenna. The 3 dBi antenna has a 360 degree range connectivity.
So, the higher the dBi, the further the reach in the horizontal plane, and you lose vertical pane. The lower the dBi, the further your can reach on the vertical plane and you lose on the horizontal reach.
Most routers come with an Omni-directional antenna. You also have to take into account that not all antennas are created equal or cable for that matter.