It depends on which synthetic and which conventional, but, in general;
Syn can last longer because it's generally 'better' at TBN retention, resisting shear, high temp stability, dirt suspension, and all the other metrics that can be used to quantify an oils performance. It's 'custom built' in a lab.
Conventional is kind of a 'close enough' botch job that will do the job but not as well or for as long.