I would plan on housing them separately. Cages are small. Even a "big" cage is still quite small. And small spaces are a problem if you are trying to safely house parrots with different beak sizes and energy levels.
Cockatiels and budgies do live in the same habitat in the wild, but there are many important differences between the Australian Outback and your living room. For example, in the wild, if two parrots have a conflict, they can fly away. Far away. So far away that they never meet again. Or maybe they will just fly to a different tree, if it was a minor conflict. But they can fully remove themselves from the situation, when necessary. Parrots will sometimes "argue" in the wild, but those fights are rarely serious because the loser gets to leave. And many fights never happen at all because, they are not forced to remain in close proximity to another bird. They choose to land on an unoccupied branch and they choose to avoid birds that they don't know and trust. In a flock, personal space is very important. You don't let just any bird touch your feathers. You don't move right next to a bird, unless you like them or want to bite them. That is how a parrot flock co-habitates peacefully.
But in a cage, those choices are taken away from our birds. We decide how big the cage will be and how much time they will spend locked inside it with another parrot. They can't leave after a fight or if they don't feel safe, because they are trapped together.
Even if they get along most of the time and seem to enjoy each others' company, everyone has bad days. You don't always get along with your roommate. Sometimes you need to give each other space or a fight is inevitable. Birds need that, too. They get tired. They get grumpy. They get frustrated. They get stressed or hormonal ... and then they get bitey.
It only takes one serious bite to lose a parakeet. I would not risk it.