It is good to say a bracha out loud so that other people will have the merit of answering Amein. You get two mitzvos: (1) reciting a bracha and (2) loving a fellow Jew – since you enable someone else to fulfill the mitzvah of answering Amein.
A bracha to which Amein was answered is a better bracha than one to which Amein was not answered.
There is a famous story about Reb Chaim Volozhner who was moser nefesh not to drink water until someone came to his house to say Amein, and G-d did a miracle for him by sending him an angel in the guise of one of his students.
Having said that, it is not modest behavior for an isha to say a bracha loudly just so that a man will answer Amein. If she is together with other ladies, then that’s fine.
The minhag in Chabad is to bless quietly, since there is an opinion that one is yotzi a bracha through hearing it and saying Amein even if the person blessing did not have in mind to be motzi the person listening. Thus, the listener will be unable to recite his own bracha later, since he was already yotzi according to this opinion.