Often, 3rd party apps that can be used as a camera offer different levels of resolution in which they capture the image. Since Instagram is a widely used, and up-to-date app, I would expect they support the highest resolution offered on your device (disclaimer: I don't use Instagram so I can't check with that app).
As long as you have the resolution setting (if available) set as high as possible then you should notice no difference between the built-in camera app and Instagram - you should not lose image quality during import either.
Otherwise it comes back to personal preference. If you take the images with the built-in camera app, then your photos are automatically in Camera Roll and can be easily saved onto a computer. Camera app is also easy to open from the lock screen.