I have never heard of a cockatiel killing a budgie, but I have heard of budgies biting cockatiel toes off! Cockatiels are one of the most doctile, gentle parrots and rarely harm any other bird, whether big or small. From what I have read, the reason they do not recommend housing tiels and keets together is because keets are more dominant and if their harmone levels rise, despite their size, they are the ones that normally harm the tiels' little toes. I wouldn't recommend them living in the same cage all the time, unsupervised. They should have supervised playtime together, and I know that cockatiels and parakeets and get along great, but I wouldn't recommend them staying in the same cage. I know some people do and never have a problem, but you never know. I have birdiesat a couple of my friend's keets, and we let them go in our cockatiels' cage to play for a while. They didn't harm each other, but the keets were bossing my cockatiels around and my cockatiels came crying out of their cage to us (babies ) so we took them out. Good luck with your birds. How long have you had them?