5.9.9.
The deaths of James and Simon, continued (1): the facts. Acts 11:28 and 12:1ff, as well as Ant. 20.5.2 describe a famine

followed by the executions of a James and a Simon, both identified as sons of Judas by Josephus, while in Acts 12:1ff Simon is given the Christian name Peter.

The difference: Josephus describes the crucifixion by the governor Tiberius Alexander in 46 AD while Luke reports the beheading by the Jewish king Agrippa I in 44 AD.

I consider that both accounts refer to the same event, with some differences. Aspects in favour of this view: the names of the executed /imprisoned men are identical; the situation is identical, with the preceding famine – we should envisage food riots and the execution of the leaders; the time is almost identical.