According to my calculations based on the table in the CRB you could make a ring of vanish with continuous invisibility for considerably less than a Ring of Invisibility will run you. Level 1 spell, 1st CL. 1 x 1 x 2,000(for continuous or use activated)x 4(duration in rounds)=8,000 GP. This as opposed to the Ring of Invisibility that is command activated, only lasts 3 minutes at a time and runs 20,000(which actually I'm pretty their math is off based on their own item creation rules, but that's a different story).
My real question is with the ring could it be use-activated and still give a continuous benefit until it was deactivated again? or is use-activated just an over-glorified Command Word?