While the FX-8320 build is in budget, the M5A78L-M LE has no VRM cooling whatsoever. This isn't an issue with an FX-6xxx series CPU, but the FX-8xxx series are notoriously hard on the VRMs. The CPU may throttle, not because it's hot but because the VRMs are roasting.
The FX-6300 is decent enough for the money and shouldn't cause any issues with hermal throttling. My dad has the FX-6300 and it's more than enough for his office browsing and Photshop work.
Personally I'd go with the i3 as it's more efficient and is current technology. Bear in mind the FX series are around 4 years old now.