If Pence challenges the subpoena, he’ll fall flat on his face. According to case law, speech-or-debate protections extend only to legislative acts, and Pence unequivocally stated his Senate role was ministerial and largely ceremonial. He’s just trying to stay in Trump’s good graces by appearing to fight the investigation.
There's no doubt that Pence is right to take this path to fight the DOJ's subpoena as the vice president indeed constitutionally belongs to the legislative branch. By dismissing Trump's alleged pressure campaign to overturn the election, Pence made it clear that he was an officer of the Senate in his own right, not an executive official subordinated to the president.
Smith is a politically-motivated prosecutor who is running an illegitimate investigation and has botched prosecutions in the past — both domestically and overseas. There’s no way anyone, let alone the former vice president, should tell Smith anything.
There's a 54% chance that Pence will be a candidate for US president in the 2024 elections, according to the Metaculus prediction community.