I may be able to weigh in here, so to speak.

I recently switched from typical wheels to 38mm depth carbon clinchers.

I would say I really notice a difference on descents, say above 30MPH.

There is a small but definite difference at moderate speed, say 22 or 23 MPH.

At "easy cruising" speed of say 18MPH there is not any real difference that I can notice.

I chose the 38mm because I only weigh 145 pounds and wanted wheels that could handle crosswinds....there were 25MPH crosswinds last weekend which were no problem.

I hope that helps.

p.s. if you can stretch your budget to a grand, consider the williams 38's which are what I have.