A wise mentor of mine gave me a little hint that I have always used and passed along to others. If the bird looks like someone dipped it in grape jelly, it is a Purple Finch (female above).
If it looks like someone dipped it in strawberry jelly, it is a House Finch (above).
Of course, there are other ways to differentiate the two. The strong white line above the eye of the female Purple Finch really helps from a distance.
The thing I've learned from banding finches is, if the bird is aggressive and bites, it is a Purple Finch. If it is pretty docile it is a House Finch. I'm not sure how helpful that one will be but it has been pretty consistent in my experience.
The other factor in an ID can be location. Purple Finches tend not to nest in my area and House Finches are all over the place in the breeding season. If it's migration season though it pays to take a close look at any finch you see.