What is a limit to the information I should put up on LinkedIn? So
that I still stand a chance to be contacted by potential employers and
at the same time, not revealing too much of myself to other people I
don't feel comfortable sharing my information with?
The limit will always be a fairly personal choice. As usual, any online posting method puts up questions of privacy as well as unintentional publicity. I would agree with you that your LinkedIn profile is similar, but not quite the same as your online resume.
For my part, here's the differences I've used - the differences are as much about the medium itself as well as the audience pool. I use LinkedIn for my personal/professional network, as well as for job hunting - so I tune the profile accordingly:
Less detail about specific positions - the verbiage below each job is far terser. I tend to skip any company-specific awards and stay close to facts. Because I also work in organizations that are highly private, I'm deliberately vague about particular projects, and focus instead on the general type of work I did in the position. In a resume, I'd tune this text for the specific position or type of job.
Much longer history - I connect with old high school classmates, college pals, and collegues from my first internship. Having connection points that I wouldn't put on a resume really helps - like High School, specific work in college (for example, being a tutor and leading a club), and internships. My resume does show my undergrad school, major, and year graduated, but 15+ years since graduation, I skip all the rest of this information on my tight 1 page resume. But finding my old friends is a tremendous value add that makes all this stuff well worth mentioning, even if the recruiters shouldn't care.
Lots more searchable facts over text - my resume paints a picture of who you are hiring. To do that, I've thoughtfully organized my information in the hopes of highlighting things that you will care about if you are interviewing me. LinkedIn is about connections - so searchable facts and hit words take precedence. I'll never get the job if the recruiter doesn't find my profile.
Those general points do get me away from a bragging-heavy (I hope!) profile. Certainly the earned qualifications stand out - like jobs, certifications and degrees - but I find these to be less controversial than saying "the leader of a 3 man team" or "subject matter expert for..."
Do I really want my information to be seen by, say competitors/rivals,
or even being checked on and judged by other people?
Entirely your call.
Certainly I am more cautious about the nature of the work I do when writing those summaries. I work in high end info sec, and my companies have very specific rules about what I can publicly disclose. Before making updates, I usually read these rules and then do my best to be clear while staying high level enough to keep out of trouble.
Similarly, because I do want to be found by friends and make a good connection, I give the summaries a read with an eye to all readers. The recruiter will only read enough to send me a mail - they don't think deeply about the text. A friend, former boss, or other colleague is likely to spend more time. I really think that anything written in good faith is likely to work out alright, as long as you stay positive and realistic. But I'll definitely say I read it with an eye to "if someone who's worked on this project with me read this, would they agree?"
