Pros and cons of each?
It was said above, Segwit wallet is for the reduction of transaction fees, also the best of signature, and in the network optimizations while the legacy wallet address is the origin of the Bitcoin wallet which is having high fees.
I think there is a misunderstanding here.
Segwit addresses cannot sign messages. This is one of cons pointed out ranochigo.
Well, it can sign messages, but there is no standard to recognize it. In practice, you cannot sign a message from segwit addresses which will be recognized by all software.
But you can with Legacy. A message signed from a legacy address will be recognized everywhere.
But, no big deal...