The best answer to this (in the short run, at least) was that the American Revolution mostly ensured that white men with some property could enjoy the right to liberty.  However, we should not ignore the fact that some benefits accrued to other white men and to white women as well.

Certainly, white men with property enjoyed the most rights.  These were in many places the only people allowed the right to vote.  Women in many cases were not allowed to own property or enter into contracts so they clearly did not enjoy much of the right to liberty.

However, we must also understand that all white people benefitted to some degree from the Revolution.  The Revolution led to the creation of a democracy.  Even those whites who were not allowed to vote did have their rights to property and to freedom of speech and religion protected.  Even those who could not vote were protected from unreasonable searches and seizures.

So, white men with property who were allowed to vote gained the most from the Revolution in the short term, but all white people had more legal rights after independence than they had had before.