I prefer this scene to be put as the ending. Because it strongly shows how contradictory Michael was, right after what he dreamt (of protecting the family), was torn apart. Sort of nostalgic feeling, full of 'what ifs', contemplating why it came out terribly with his family.
As a bonus it also shows how Fredo was the only one not being furious and questioning Michael decision to be enlisted. And there Michael was, frowning how he ended up making order to kill own brother.
This is a very sad flashback scene for me.
I agree with Turnbull that the current version fits better. More powerful. The absence of Vito plus the 'Happy Birthday' greeting and chanting on the background made it even powerful.