Importance rhymes with:
acceptance, acquaintance, admittance, assistance, capacitance, coexistence, consistence, constance, distance, existence, impotence, inadvertence, incompetence, inductance, inheritance, insistence, instance, omnipotence, outdistance, persistence, pittance, quaintance, reluctance, remittance, repentance, resistance, resistence, self-subsistence, sentence, subsistence, substance
Importance sounds like:
imparting, importing, imprudence, inbreeding, inebriating, infuriating