I had a ct angiogram of chest with contrast and now my dr wants me to have one without contrast. i thought with contrast was always better?

Not necessarily: Ct angiogram is a study which uses contrast to enhance blood vessels and so the timing of imaging relative to imaging will vary depending on intended vascular structure. Non-contrast ct, especially high resolution would be used to evaluate the lungs. Repeat ct without contrast may be used as a follow up study as well, to avoid repeated use of contrast.

With and without: Calcium looks just like contrast on a ct scan. Doing a study with and without will let you see what was simply calcium and what could be blood flow ( contrast is in the blood stream so represents blood flow ). It can be very important to differentiate between the two.