The difference is that Assange did not simply ask for asylum. He agreed to go through the British Court system including posting bail under the solemn promise to obey the court.
Only when he lost did he go for asylum. Sincere asylum is not "Plan B."
That part, jumping bail by walking into an embassy, isn't all that unusual. China is worried enough about it that they sometimes shadow politically sensitive detainees who're out on bail to make sure they don't get close to any western embassies in Beijing.
I assume that would be a common trigger! Until that point, they may hope to be acquitted and not have to flee the country. For example, Chen Guangcheng escaped house arrest and fled to the U.S. embassy. The Chinese were not happy about that, and applied pressure, but they didn't send police into the embassy.
To receive bail, you must pledge to return to court and be bound by its decisions. Assange broke his pledge when the court ruled against him.
You can choose asylum or you can choose to let the court decide. Trying to get the best of both worlds is mere gamesmanship and lacks any pretense at integrity.
This is why, for example, Roman Polanski's lawyers have been refused a hearing on his matter in the US. You have to choose between being a fugitive or being tried in court. You don't get to say "I'd like the Court to find me innocent before I stop being a fugitive."
Only when he lost did he go for asylum. Sincere asylum is not "Plan B."