The H1 and Title Tag can be the same but the issue that comes into play is whether or not the H1 tag provide a good user experience for the onsite content if it is the same as the Title Tag.
Take this post's Title Tag for example "Can H1 and Meta title be exactly the same ? Why not ? | Moz Q&A". If you put that as the full H1 it would not be as good as:
Can H1 and Meta title be exactly the same?
or
Can H1 and Meta title be exactly the same ? Why not ?