3rd Person limited sounds like what you're talking about - where you follow very close to one character, perhaps even reading his thoughts, but not anyone else's.

3rd Person omniscient can read everyone, everywhere, and is not in vogue at the moment, though you do see it occasionally.

1st person follows similar to 3rd limited, except it is very very intimate and you definitely know what the person is thinking and feeling.

3rd limited is not just one character if you choose to involve others. I have a great book on it,
http://www.amazon.com/The-Power-Of-Point-View/dp/1582975248/ref=sr_1_1?ie=UTF8&q...

You really need to choose which one is best for your story - and there are more points of view than just the couple I listed above. It might also have to do with how you write. I love Jacqueline Carey, but I find her much more compelling in 1st person than her 3rd person books, one of which I could never get past page 10. I'm sure other authors do much better in 3rd than 1st, but I can't think of one offhand.