There is a lot of speculation as to which functional group is more polar, I've read a lot around this on the web and I can't decide which one is actually more polar? Can someone help because I need to know how to identify the most polar groups in drugs to create some drug monographs.
However, this neglects additional factors relevant to the discussion: ionization and solvation. Under physiologic conditions, carboxylic acids are generally deprotonated resulting in a formal charge separation with a -1 charge delocalized across two oxygens. Depending on what parameters you are concerned with, this may be a more profound effect than the difference in gas phase polarity.
A carboxylic acid would be more polar. Amide bonds are essentially how proteins are bonded together, and are the less-polar condensation product of an acid and and amine. One way to think of it is, amino acids are more polar, and are converted to proteins, which are less polar. Polarity may change with pH, but is the case at least for the only pH that you'd care about, which is that of the human body.
The primary amide is more polar. The nitrogen and oxygen are conjugated, giving the C-N bond partial double bpnd characteristics, meaning it forms stronger H bonds. Also the difference in electronegativities between oxygen and nitrogen mean it is more polarisable. These characteristics are reflected in the boiling point and dielectric constants of amides vs carboxylic acids.