How do Hermione and Hedwig act towards each other? When you had the aggressive budgie, was one or both a female? Generally the females tend to be more aggressive and two males should be able to at least tolerate each other in an open space where one has the chance to escape if he wants to.
I have two budgies, one American and one English. The English, Winston, is still fairly new to our home and new to everything (out of cage time, being around people, etc.). So there are times when my English budgie gets overwhelmed and doesn't always want to play, and when this happens he flies away from the other (more persistent) one. I do currently keep them caged separately because Winston does not like being in closed spaces with Jerry - he just needs to escape sometimes, and every time that they are both in the same cage Winston immediately flies out to get away from Jerry. If they prove that they both really want to live together, we'll let them of course. But they both seem to enjoy their alone time as well.
One of my cages does have a divider. I've thought about housing them in this cage together WITH the divider, but have not tried that just yet. But this cage was also fairly inexpensive for a larger budgie cage, I believe it was at Petco for $40.00 (in case you're on the lookout for a new cage with proper bar spacing):
