Every-time I've put on new tire(s) of the exact same size and brand (25c 4000gp II) they feel faster and more supple with better handling. This may be real vs. mental given the aging and wear of the rubber which on the old tire is cracking and feels harder.
An well worn tire will also have more rev's per mile resulting in a faster speed readout (if not gps) - about 0.5%