Bullet or Paragraph Resumes?

The preponderance of advice online, both for MBA application resumes and employment resumes, is that bullet points are preferable. They constrain the writer to succinctly summarize achievements into single lines and offer a frame of reference for resume readers and interviewers (your third bullet point here, for example).

However, I have noticed that many MBA candidates use paragraph formats on their LinkedIn pages. These are not paragraphs in the normal sense but essentially sentences that could be bullet points arranged into a thematic paragraph. I feel that the linkages between these points align better when arranged in a cohesive paragraph as opposed to individual bullets, but I am concerned that this format is non-traditional and may look like the dreaded 'block of text' which discourages readers. I have noticed the same format in sample resumes on non-MBA school webpages (for example, Harvard Law).

What are people's thoughts on this?

Thanks.