Below is some difference between Eureka 3670G and 3684F:
Eureka 3670G vs 3684F
images from manufacturer

HEPA Filter:
The Eureka 3684F comes with HEPA filter traps tiny dust, pet dander, and other small particles, makes the exhaust air cleaner.
The Eureka 3670G does not include a HEPA filter.

Pet Hair Attachment:

The Eureka 3684F comes with a PET Power Paw to pick up pet hair from rugs, carpeted stairs, upholstery, etc.
The Eureka 3670G does not have this PET Power Paw.

Price:
The Eureka 3670G is cheaper.
The Eureka 3684F is priced at $149.99 on eureka.com.
The Eureka 3670G is priced at $79.99.
( Prices checked on 03-20-2013)

Color:
The Eureka 3684F is purple and black.
The Eureka 3670G is in yellow and black.

If you know any other difference between these 2 Eureka canister vacuum cleaners, please share below to help others make a right buying decision.