PNG-24 / Save for Web - File size too small

As a visual designer, I am doing way more Web-digital graphics these days, and no matter how much I thought I knew, something comes up and technology still perplexes me. I was requested to output a Logo from Illustrator (EPS) as both: jpg and a transparent PNG. So I took them into Photoshop. Comp size was: 35p X 100px width 72dpi.  The jpeg came out fine with about 18KB of meta data, however no matter what settings I use for PNG (Save for web: PNG-24/Bilinear-Bicubic, etc.) the PNG-24 only holds about 4 KB of data and looks kinda junky...what gives?? Shouldn't this file size be much higher than the jpeg? Can anyone clue me in - what could I do better- different-any suggestions? Thank you kindly!