I would not ever keep two different species in the same cage, and cockatiels are actually particularly ill suited to this. As somebody else pointed out, Cockatiels are MUCH larger birds than a budge, a cockatiel could very seriously injure a budgie without much effort, maybe even on accident. However, Cockatiels are actually a fair bit slighter in build than other parrots of their size- a small conure, while the same length as a cockatiel, is a much stockier bird that can again, severely injure the Tiel without much effort, and maybe even on accident.
It's also important to realize that birds are different species- not just varieties of the same species. A labrador can get along with a great dane because they "speak the same language"- they're both dogs, just bred for very different characteristics. Sort of like a thoroughbred and quarter horse are both horses. But a donkey is not a horse, it doesn't speak horse, it has very different characteristics from a horse. In the same way, humans, orangutans, and gorillas are all apes. But you wouldn't be able to communicate with an orangutan in your house, and he could easily kill you, even on accident, just by trying to play like an orangutan.
Likewise, birds are vastly different species, from all over the world. They don't speak the same languages, have the same behaviors, or even eat the same diets.