I know this is a late reply, but it might be useful for anyone else who is looking for an answer to this question in the future.
I have owned both a Budgie and a Bourke, but only one of each, so my experience is not final.
My budgie was loud and excitable, even in her old age. She loved to play with bells and mirrors, and even had a habit of dancing (Bobbing her head and scuttling along the branch) if she liked the music we played to her.
However, she was temperamental and quick to become aggressive. She strongly disliked any other budgies and so we kept her with the cocktails, giving up on finding her a mate. She was very good with raising our baby cockatiels, which we breed and sell, and could be very gentle when she wanted to be.
Our Bourke, on the other hand, is very quiet. It is rare to hear him twittering away, and when he does we all go silent to listen to his beautiful voice. He responds well to my attempts to mimic his call, and likes to twitter to me. He rarely clashes with the other birds, happily keeping to himself. He is great with the babies, watching them and running around on the tables and floor with them when they can't fly. He is nowhere near as playful, and we can not pick him up. If he feels like it, he'll land on us, but we can not get him to in any way.
In short, from my experience, the budgie is like an extrovert; Playful, loud, social, cuddly and so on.
A bourke is like an introvert; Quiet, gentle, and happy to sit.
There really is little in common, personality wise. There are pros and cons to both. If you want a loud, playful bird that you can watch, take videos of to post online, or teach to talk, a budgie is for you.
If you want a gentle, quiet bird that is happy to be left alone with other birds, occasionally sings quite beautifully, and is a generally tidy bird, I would recommend a bourke.
Again, they vary bird to bird. I cannot guarantee that they will all be like mine. My budgie, or example, ended up acting much more like a cockatiel the older she got, going as far as to mimic their whistles. That is likely a large influence in her behaviour.
But I hope this helps someone to pick which they would prefer.