Here is my take on the Brava. I had a Brava 4 that was a 2016-2017. I always had a problem with it being too tight with the Vega reds or YLC's when the track was rubbered up or the weather was really hot. When the weather was cooler in the spring and fall it would be fine. Or if the track was green in the morning or after a rain it would be fine. On the harder tires it was fine.
Right before I sold it to my brother I had it working ok in the warmer weather. I can't remember what I changed, but if i remember right I was playing with the caster and running the rear real narrow. My brother raced it in Florida for awhile and he was able to run near the front with it.
So it can be made to work fine, but it took me awhile to figure out what the chassis needed and I only race once or twice a month.
I've never driven the K3, but looking at the chassis it doesn't look as stiff as the Brava 4 I had. But my Brava had the 2 cycle style brakes and looked slightly different than the 206 version on the website now.
With the K3 you could also run the Ignite spec class as well at the regular 206 class. For 206 I think the K3 would be fine. I actually preferred the slightly cheaper components of the K3. Like the brakes. I like the old style MCP's compared to the Euro brake setup. I did like the sniper pill setup, but it kind of needs the laser system to so you can check settings. The pill system works just fine.
What brand of kart has local support in you area?
I hope that helps a little, but I don't think going with the K3 would be bad. I think either kart would be fine for you. The Brava 206 is just going to have a little better components, but like I said I don't think you need any of that stuff.