Other than one being to lick, any difference between the 2 for underestimating?
舐める is slangy and should be avoided in very formal contexts. Its meaning is closer to "to look down" rather than "to underestimate." 舐める often also has a connotation of behaving disrespectfully/insolently to someone/something.
侮る is a relatively literary word and typically used in a set phrase "侮るなかれ" or "侮ることなかれ". It's probably safer than 舐める, but still has a connotation of making light of something/someone.
過小評価する is a neutral and politically safer word for "to underestimate," which does not imply any disrespectful attitude.