https://www.delawarenaturesociety.org/blog/how-to-tell-house-finches-vs-purple-finches-apart/

It is harder to distinguish female House Finches from female and young male Purple Finches (males hatched the previous summer) as they are both brown and streaky. However, female House Finches have a plain brown face, whereas female and young male Purple Finches have a broad white stripe above their eye and a dark brown cheek. Female and young male Purple Finches are also more heavily patterned than House Finches and their plumage is darker and more chocolatey-brown. The female House Finch also appears to have a smaller, ‘beady’ eye.


Female House Finch. Note plain brown face and beady eye


Female or young male Purple Finch with white eyebrow.