The short answer: Piezo is great for very simple recordings, while Audio Hijack is great for users who need more power.
Looking for more details? Piezo is designed for simplicity, making it a snap to record audio. It's easy to use and eminently affordable. Audio Hijack, on the other hand, is much more powerful than Piezo. It offers many more features and has a correspondingly higher price.
Here's a partial list of features found only in Audio Hijack:
System Audio recording, to capture all audio from your system at once
Expanded recording options & lossless recording formats
Configurable voice chat (VoIP) recording options (See this article for more details)
Realtime audio processing adjustments and effects
Timed recording, using built-in scheduling
Piezo and Audio Hijack each have their place, and you might like one or even both. If you're still not sure which you'd prefer, we encourage you to download free trials of both Audio Hijack and Piezo. Using the trials should help you determine which audio recorder is best for you.