That's an interesting question, and I'm curious the different responses you are going to get.
I'll just say right out of the box, which I'm sure you already know and get, it's kind of a tough question because not all dome tents or tipi's are equal in quality of product, materials, components, etc. I've seen some of each that I wouldn't be trusting for my safety or life on a remote drop hunt.
That said, here's a statement about a specific dome tent and a specific tipi. I have a Hilleberg Staika dome tent...it's a four season tent that I have used hard for eight years all over up here in Alaska, including Kodiak. That tent has proven itself bomb-proof, over and over again...period. I also have a SO 4-man tipi that I've also used up here for the past four years. We primarily use it for a day shelter on extended drop hunts to get out of the wind and rain, but we each sleep in our individual tents. There have been many times that I have gotten out of my Staika in the morning, not expecting to see the tipi still standing because the winds were hellacious that night...but each time it's right there, still standing and fully intact...each time, without failure. That said, I use good stakes for both my tent and tipi, i.e., stakes designed for tundra.
So, given a comparison of that dome tent and that tipi, it's looking like it just might be a draw when answering the specific question, "Which performs best in high winds." However, I'm still going to choose to sleep in my Staika under those conditions.