Fun fact: The X-Files production team foresaw the coming of 16:9 home entertainment, so they made some effort (increasing with later seasons) to try and "protect" a 16:9 frame, which allowed for an unusually good 16:9 Blu-ray restoration. [ https://www.tweaktown.com/reviews/7499/look-inside-the-files... ] I learned this from the older X-files DVDs, which have some unusually good special features.
The article mentions that Mad Men was already in 16:9 so the issues are unrelated to re-framing.
That said, I think letterboxing is a better choice than trying to recompose a shot for a different aspect ratio if it wasn't accounted for initially (eg: The X-Files). And even then, the shot selection and composition would have been different had the aspect ratio been initially different (like TXF's 16:9 versions leaving the edges of the frame largely unused).