Like Harold says, it can depend on the brand and model.
I happened to be discussing Octo's with the Training director at the shop that I patronize and he made a good point. It is in your best interest safety wise to ensure that the secondary air source (your octo) is up to the same performance standards as your main regulator. And even better is to have the same second stage as an octo that you have as your primary.
If you think about it, this makes sense. If your dive profile includes considerations beyond recreational limits (deeper than 60 feet on standard air), you want to make sure that your octo can handle the same demands as the primary.
Therefore, I'm making the case that when making your gear purchases, DON'T SKIMP ON YOUR OCTO. Consider getting the same second stage as your primary.