It is completely understandable that some people who are new to reviewing manuscripts may lack confidence in their reviews and wonder whether they are commenting on the "right" things in the "right" way and in the "right" amount of detail. It might be comforting for these uncertain reviewers to see the comments of the other reviewers to gauge whether they are on track with their own review.
Consider, though, that the content and styles of reviews vary a lot from reviewer to reviewer because reviews should vary a lot. It isn't necessarily such a good thing, then, if your review comments correspond well with those of other reviewers. In fact, if you commented on completely different things that the other reviewer didn't consider or notice, this could make the reviews even more useful to the author(s) and editors.
As an editor, I try to select reviewers who will examine a manuscript from different points of view. Of course different reviewers should be able to detect any major flaws in a manuscript, but beyond that, I want different reviewers to comment on different aspects of a manuscript. Otherwise, why get more than one review?
Doing a review is not a test that you pass or fail as a reviewer. You are providing a service to your professional community by sharing your expertise.
What should a review contain?
Reviews should provide a thorough and constructive critique of the content of a manuscript, focusing in particular on the data, analysis, and/or ideas that form the basis of the work. You should consider whether you think the interpretations are justified, making it clear whether something is objectively "wrong" or whether you just don't like it.
I am not impressed when a reviewer says "This is wrong" about something in a manuscript but doesn't explain why and doesn't provide any suggestions about better alternatives or ways to get at a not-wrong result. If you want your review comments to be considered by the editor and the author, you need to back up any criticisms as much as possible. It also helps to be polite. Your comments will be taken more seriously if you write "I do not agree with the interpretation that A follows B, and suggest instead that..." as opposed "These people are seriously stupid if they think that A follows B."
Note: Some reviewers write their reviews in the active voice, directly addressing the authors as "you", as in "You should consider deleting that entire section that starts on page 17"; others refer indirectly to "the authors", as if the comments are addressed primarily to the editor, although of course the authors will read these comments. Perhaps the custom varies in different disciplines or different journals, or maybe it is just a reviewer personality thing.
In your review, if you are going to suggest the addition of a citation of one or more of your own papers, you should explain why this should be done. As a reviewer, I typically comment on citations of my own papers, or lack thereof, only if (1) a paper is mis-cited (i.e., my paper on purple kangaroos who live in lunar craters is cited after a statement noting that green rabbits live on Neptune); or (2) if there is an egregious omission (i.e., a statement that purple kangaroos live in lunar craters and then no citation of my work whatsoever, despite the fact that I have published extensively on this topic and no one else has).
Reviewers should, to some extent, consider the manuscript as a completed thing and only suggest the addition of new items (particularly those involving new research activities that may be costly in terms of money and time) if those items are absolutely essential to the manuscript; i.e., without them, the paper is not publishable. If you truly believe that a paper is not publishable based on its current content, of course you should state this in your review and back up this opinion with reasons, but if you just think the paper would be better with more data, make it clear that you are making a suggestion, not pointing out a fatal flaw.
This is where an editor can play an important role. In many cases when I see this type of do-more suggestions in reviews, I tell the author that I think this is an unreasonable suggestion and they do not need to address it in their revision. In other cases, I concur with a reviewer and tell the author that their paper is not publishable without this additional work; fortunately these cases are quite rare.
It is also very useful if a reviewer comments on technical aspects of a manuscript, particularly those issues related to clarity. Does the organization of the text make sense or does it interfere with your understanding of the major points of the paper? Is the paper too long/too short? If not, what is a better way to present the information?
I understand if a reviewer does not want to take the time to fix the writing problems in a manuscript, especially if there are a lot of problems. I don't like doing this as a reviewer and I find it annoying as an editor, especially if at least one of the co-authors is a native English speaker. I am not paid for my work as an editor, and co-authors who are able to fix their own writing problems should take the time to do so before submitting a manuscript and expecting others to clean it up. If none of the authors are native English speakers, of course I can and do help with writing issues, but I am always grateful when a reviewer takes the time to do this as well.
To those who lack confidence in their reviews: don't worry. Just do a careful job of reading and commenting on the manuscript, and there is a very good chance that your review will be helpful to the author(s) and editor.
Keep in mind that your main job is not to point out new and different research activities that the authors should have done or could do, and focus on what is in the manuscript. Provide both general and specific comments (including noting what you liked about the manuscript, if anything, not just what you didn't like), note any problems you find, make constructive suggestions, and don't take too long with your review. Also remember that by reviewing a manuscript you are doing a great service to all involved, and perhaps learning something interesting, so don't stress out, just dive in and write out your comments.
10 months ago