A woman's 'chance in life' depended almost entirely on whether she could make am happy/prosperous marriage, as there were so few opportunities for women to earn a reasonable living for themselves. A man had many more opportunities to prosper if he had intelligence, energy and luck.

Apart from that though, I doubt that gender would have been the determining factor in the relative life chances of illegitimate males and females. I think family support and wealth would have made much more difference.

Here's what Mr Knightley has to say about Harriet Smith in 'Emma' :-

"What are Harriet Smith's claims, either of birth, nature or education, to any connection higher than Robert Martin? She is the natural daughter of nobody knows whom, with probably no settled provision at all, and certainly no respectable relations. She is known only as parlour-boarder at a common school. She is not a sensible girl, nor a girl of any information. She has been taught nothing useful, and is too young and too simple to have acquired any thing herself. At her age she can have no experience, and with her little wit, is not very likely ever to have any that can avail her. She is pretty, and she is good tempered, and that is all." (Ch 8)

His objections to Harriet are as much to do with her lack of money ('settled provision') and her lack of respectable relations as to her illegitimacy. Emma's view of the matter is much the same by the end of the novel:

"Harriet's parentage became known. She proved to be the daughter of a tradesman, rich enough to afford her the comfortable maintenance which had ever been her's, and decent enough to have always wished for concealment. Such was the blood of gentility which Emma had formerly been so ready to vouch for! It was likely to be as untainted, perhaps, as the blood of many a gentleman: but what a connexion had she been preparing for Mr. Knightley, or for the Churchills, or even for Mr. Elton! The stain of illegitimacy, unbleached by nobility or wealth, would have been a stain indeed." (Ch.55)

Among the aristocracy and wealthy gentry there are numerous examples of illegitimate children, both male and female, who were acknowledged by their fathers, given an education suitable to a lady or gentleman and financially provided for, who went on to live prosperous lives, make 'good' marriages and be absorbed into society. Wealth and noble connections bleached the 'stain' of illegitimacy very effectively for both males and females. (I can provide examples if needed.)