Oh, i would say that they could hardly to better than the first child they had. Anne wouldnt loose her head and the BBC-show Tudors wouldnt be made.
There's quite a number of possibilities. The most quintessential difference is probably that Henry VIII wouldn't get rid of a wife that evidently could produce sons. Even if that son would have died early, Henry would have known that his wife is capable of giving birth to sons. Therefore, he'd never have executed Anne, and she would might have had influence him subsequently. Well, she had influence on him, in contrast to Jane Seymour, and giving birth to a son would have secured her position beyond belief. That is, after all, is what brought Catherine of Aragon into trouble.
Was Henry happier with Anne than with Jane Seymore that he loved dearly until the day he died according to wikipedia
What do you base that conclusion on that Henry VIII was happier with Jane Seymour than he was with Anne Boleyn? After all, Henry VIII loved Anne Boleyn so much that he patiently waited several years until breaking up with Catherine of Aragon and marrying Anne Boleyn. What made him unhappy was the fact that Anne Boleyn didn't give birth to a son.
One major effect of this would be that Bloody Mary is out of the equation. She wouldn't be high on the priority if there's a son by Anne Boleyn (note: he may even die early). In OTL, Elizabeth was considered a bastard, and hence lower in priority of inheritance than Mary. In the ATL, Mary will be basically out of the equation.