I am running AEM 6.0 and have installed Service Pack 3 on my author instance.
Should I also install the same on my publish instance? Are there any guidelines whether I should install the same packages on all instances?
Thank you in advance.
You should be following the release notes install instructions
While it doesn't say so explicitly, yes, you would want both author and publish to be running the same code.
Although, do read the requirement for a deployment with MongoDB and multiple instances.