"What's he like?" is a catch all term requesting the other person to describe the 'he' of the question, but it places no limit on what is described (i.e. it can be answered with "he's tall, dark and handsome" as well as "he's witty, thoughtful and diligent").
"What's his personality (like)?" ('like' added as it's more natural to say it in conversation) relates to said 'his' personality and from above would only be answered as "he's witty, thoughtful and diligent" out of the two answers given.
In casual conversation though, they usually (but not always) mean the same thing.