I think that there has to be some qualifications here. The first would be that the relationship between April and Frank is not very analogous to that of Daisy and Tom. The former are married to one another. Tom and Daisy are not outwardly struggling in their marriage and this is significant because it puts their relationship in a different setting than the one shared by April and Frank. In the world of Tom and Daisy, the ambition is fundamentally different than the one that April and Frank possess. Whereas Tom and Daisy's world is predicated upon social advancement and a rather superficial view of the world, Frank and April literally understand that there is a hollowness in their own world and seek to do whatever they can to try to avoid it. Perhaps, the common link between both settings is that Tom and Daisy are unable to gain any sort of lasting happiness, despite his desire for social acceptance and material acquisition. However, this seems to be fine for both of them, as neither of them are willing nor ready to engage in a reflective analysis of their relationship. This is opposite of Frank and April, who understand the problems that exist between them and around them. In this manner, Frank and April try to find happiness away from America, but in the end, they are unable to outrun the hollowness that exists, something that is a constant companion for Frank when April dies.
The previous response to this question seems to have taken for granted that when you asked about "the characters" in these two novels, you meant the married couples. I think, however, that this question is best addressed in regard to April Wheeler from Revolutionary Road and Jay Gatsby in The Great Gatsby.
April Wheeler's ambition is to have a more interesting and "special" life than her contemporaries. Once an aspiring actress, the novel finds her as a suburban housewife. In an attempt to prove that she is "better" than the others resigned to suburban American living at the middle of the twentieth century, she convinces her husband that they should move to Europe. Unfortunately, circumstances arise preventing the family from making the move and April's inability to meet her ambition leads to her ultimate destruction.
Jay Gatsby's ambition in The Great Gatsby is motivated by his love for Daisy. Similar to April's unrealistic fantasy of an exotic expatriate life, Gatsby's obsession with Daisy is unfounded--she doesn't even truly return his affections. Much as April's inability to meet her ambition leads to her destruction, Gatsby's realization that the life he desires with Daisy will not come to to fruition ultimately leads to his destruction as well.
In both instances, when the ambitious goals of a single character become their primary focus in life, the end result is never positive. In addition, in both instances, their aspiration is dependent upon the actions of another person (for April, her husband Frank must support the family's move to Europe; for Gatsby, Daisy must be willing to leave her husband for Jay). When one's destiny relies on the actions of another, it almost always leads to a downfall.