For bonds that are otherwise identical, the one exhibiting the highest level of positive convexity is most likely the one that is:
When interest rates rise, a putable bond is more likely to be put back to the issuer by the investor, limiting the loss of value and giving the bond more positive convexity than an option-free bond. In contrast, a callable bond is likely to be called from the investor when interest rates fall, limiting the gain in value and giving the bond negative convexity.