Jack (John) Worthing and Algernon Moncrief are two very different men, but they share more than either would probably want to admit. To answer your question, Jack would like to think that he is more serious and more upstanding than Algernon. He thinks that hispretending to be Ernest in town in order to escape the moral example he must set in the country is different from what Algernon calls Bunburying. But Algernon is right -- Jack is a confirmed Bunburyist. Both men have created a persona that allows them a ready excuse to get out of obligations they would rather not endure.
In this same vein, Jack lives a more serious life. Jack lives his life knowing that he has obligations to others, while Algernon lives entirely for amusement. He is always eating. He goes to the country and meets Cecily just because he heard she was pretty and knew that it would drive Jack completely crazy to have "Ernest" come to visit.
Jack is, at least in Act 1, more genuinely interested in marrying. Algernon says absolutely nothing positive about marriage -- in fact many of his best lines are insulting the institution. Interestingly though, once he meets Cecily, he is completely caught up in the idea and fights for the right to marry (of course, her wealth may play no small part in that).
Jack has no family connections in high society, while Algernon is the nephew of a Lord and Lady. Jack does have wealth though. Algernon is broke. They seem to be friends for what each can offer the other -- Algernon introduces Jack to all the right people while Jack picks up the tab for dinner.