I agree that part of the big difference between Elizabeth's situation and Charlotte's was age, 20 versus 27. Also, there's Elizabeth's beauty and Charlotte's lack thereof. Charlotte is repeatedly described as being "very plain," and Elizabeth is described as being pretty, a "famous local beauty," and even a grumpy Darcy admits from the start that she is "tolerable" (even if she's not quite handsome enough to tempt him to dance, something he hates). Elizabeth also had another potential suitor (Mr. Wickham), who she seriously contemplated despite his lack of fortune.
Jane Austen gives good examples of all the many unhappy fates a woman can face through marriage. Fanny's mother, in Mansfield Park, married a poor man out of love, and ends up living a desperate existence, so much so that she sends one of her most promising daughters to live with relatives out of hope that she might better herself. Mr./Mrs. Bennet make a poor choice in marriage and both become worse through their association with each other and are miserable in their marriage, if for the most part well-off enough in money. And Miss Bates shows us the fate of a woman who never marries and who sinks lower into poverty every year. Of course, Elinor and Edward Ferrars marry for love, knowing that his prospects are moderate at most, and they are able to make a happy marriage out of it. So perhaps some of it depends on the character of the people (I believe Fanny's father drank) and also exactly *how* bad their situation was.
I once read a book that was about Catherine of Aragon, in the years from when she first met Prince Arthur through her marriage to King Henry VIII. During the period after Arthur's death, when it was undetermined whether she had truly been "married" to Arthur (and thus whether Henry could marry her or not), she was living in genteel poverty. I'm not sure how accurate the book was, but it showed the interesting quandary of being desperately poor and hungry, and yet unable to get a job or do anything to bring money into the household because it was work, and you weren't allowed to do it. Catherine and her ladies in waiting basically survive by selling off bits of the house they're living in, and they're constantly cold and hungry. Genteel poverty may sound sort of ridiculous in a "okay, seriously, get a job!" way, but social rules were stricter in those days and it simply wasn't permitted to just "go out and get a job."