For now, both models co-exist well---and most likely will continue that way. However, Amazon is pushing its subsidized hardware model and if an entire industry goes that direction it will put pressure on the iPad mini.
When Apple launched its iPad mini it took direct aim at the Google Nexus 7. The argument was that the iPad mini was worth the $329 price tag, which was a bit high to a few analysts. Amazon is working the perception that the iPad mini price is too high.
All Amazon has to do is be in the same neighborhood as the Apple hardware features. Cheaper prices combined with a strong ecosystem may take care of the rest.