Which approach to studying is better? This is not a usual question on this site, but I think it is appropriate nevertheless since I believe that members of this forum have vast experience on studying and all things that affect studying.

I am a student and I have a "problem" that's basically this: when I start studying something I feel unpleasant and restless if I am not completely sure that I understand the content being studied. This sometimes leads me to spend "too much time" on a particular subject and one might argue that it is a waste of time. My personal opinion is that this is the only way to study, I don't go to the next topic unless I have completely understood everything that's presented and unless I've come up at least with one question that I have to resolve in order to proceed. Sometimes the number of questions increases and usually that's what prolongs the studying of that particular subject. 

However, many of my fellow students seem to be satisfied with just a basic understanding of the topic, and the questions that are keeping me from continuing, often don't bother them at all.

What is the better approach to studying in your opinion and why would that be? Am I being too perfectionistic or am I just trying to have a complete understanding of the topic?
It is good if you can understand something completely and thoroughly. However, there comes a point where most of us must leave gaps and accept that the gaps will fill with extended experience and exposure, over time (technical term: "by osmosis"). Failure to accept that gaps need sometimes to be tolerated can lead to collapse of careers. 

What you need to judge is how fast you are moving - if you do not trail back too much with respect to what's required in your duties, I would not worry too much. Good understanding is a worthy cause and will pay dividends later on. However, when you fall back or fail to address important aspects of your studies (or repeatedly fail, through perfectionism, to submit reports/works/papers on time), then you should consider ways to get a coarser, higher-level view of what you need to learn and start to leave gaps.

Hopefully these criteria will help you to judge at which level you may want to operate and to switch between levels when required.