In comparing the events of Isaiah 7, and 2 Kings 16, it does appear that their accounts are similar. They are also different in the way that you would expect from the authors. Isaiah account is from his perspective sharing what God has said to Ahaz, and encouraging him "do not fear". It also accurately predicts the invasion of fall of Judah and Jerusalem. The 2 Kings version have been edited by the Deuteronomist Writer(s) uses the opportunity to once again point out how King Ahaz "did not do what was right in the sight of the Lord", and thus concludes that this is the reason for Judah falling. They are the same story, but emphasize different aspects of what happened. Isaiah is a prophet therefore his telling is about prophecy, and 2 Kings is about a Deuteronomist view of Judah's history.
The other reason that Isaiah was present during this episode, has to do with the names of Isaiah's children. In Isaiah 7, we read about his son, Shear-jashub, which means 'a remnant shall return'. This wordplay gives a hint to what is to come both in the destruction but then the return from exile.
We also see that the writer of Isaiah, gives detail like the names of the Kings of Aram and Israel. Giving this type of detail tells us the author was concerned about historical context to the story. There are times, especially in the Deuteronomistic style that that message is more important than being historically accurate. See 2 Kings 5, the story of Naaman does not mention the names of the kings.