Same but different, sorta kinda, but not really.

I think that the two stories are drastically different even though they are both detective stories. Gender certainly plays a role in the way the stories are told, but let’s keep in account that Sherlock Holmes is a professional detective that has had great success in his profession. It is the thing he loves above everything else. It is referenced throughout that he doesn’t care for the money, he more so desires the challenge and satisfaction of solving mysteries. While he and Watson are fearlessly looking for answers in their story, Helen and Mrs. Peters are stumbling into clues as they tend to Mrs. Wrights kitchen and collect items to deliver her at her place of detainment.
These two ladies are not detectives; they have no intentions of solving any crime whatsoever. One is there to collets the items for Mrs. Wright the other is there to keep her company. Mrs. Hale even states as they converse about the quilt, the bird, and cats “If they’re going to find any evidence, I wish they’d be about it, I don’t like this place,” Pretty Ironic. It is by luck that they come across the clues they do find and by female intuition that they piece the puzzle together. So in their case they were two non-detectives who assumed what had occurred, a mystery solved unintentionally. If the story had started out stating that the two ladies were going to take it upon themselves to find out what happened there would have been a drastic difference in the story but maybe it would have read more like the Sherlock tale.
I don’t believe that if Sherlock had been put on the case of the murder of Mr. Wright and had come to the exact same conclusion, that Minnie Foster had suffocated the life out of her husband to avenge the death of her beloved bird, he would have hid evidence in an effort to keep her out of prison. I believe that regardless of how he felt, he would resist the temptation to play the role of juror and kept to his role as detective.
But that brings up another point; Sherlock wouldn’t have done so because his profession demands that he stay impartial. But Helen and Mrs. Peters aren’t professional detectives, they’re housewives. Housewives just like Mrs. Wright who empathized with what she was going through because they were going through or had gone through similar events to a lesser degree.