Both these apps seem to be apps with ‘similar functionality’ and I think the developers of the apps consider each other competitors. Both allow users to share pictures, both allow applying interesting filters to pictures.
Usually, you’d be inclined to choose either one, but after using both, I think I’ve found enough reason to use both.
There are some fundamental differences between both apps.
Instagram: All pictures get posted to public domain – meaning anyone, and everyone can see it. Yes you can also opt in to share your pics over Twitter, Facebook, Flickr, etc. But you don’t have the ability to suppress it from being shared publicly.
Path: Only friends you have chosen to share your ‘Path’ can view the pictures. You can also share it with those who are not on Path. In other words, you have control over who can see your pictures.
The difference between these two help me decide which app to use.
I like taking photographs, not so much as a hobby, but as an interest in seeing and taking photos. So, there are some pictures that are taken which are purely for the love of framing a scene and capturing it ‘on film’, and then there are pictures which are taken for the love of people and capturing moments you share with them. The latter is more private and not so much for public domain.
So most of my pictures taken out of interest in photography are posted in Instagram, where everyone, including my friends can see, but pictures that are of family or more private, get posted in Path, where only my ‘white’-list’ of friends can see.
Of course, there will be the occasional deviations from this rule 
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