Vico:
It is less likely for an eastern Catholic transfer to Latin Catholic church to be approved.
Being declined in the 21st century is
very rare in either direction. I’ve heard, only on CAF, that it happens sometimes, but I’ve never heard a report of being denied.
Today, the process is the same in both direction. If someone’s priest verifies that he has been an active member of that congregation for a period of years, both bishops will approve.
I’ve also never heard of someone switching EC to EC. I suppose it happens; I just haven’t heard of it.
Also, it can only be done once, but can be undone. This is why I’ve never formally petitioned–I would switch to melkite, but they don’t have the presence here (although I’m on the planning committee for the Melkite outreach here).
Depending upon territorial overlap, either the Congregation for Oriental Churches or the Holy See gives consent
but it doesn’t really go there any more; it’s now just the two bishops involved (I think this change was a decade or so ago).
Also, until some point in the 20th century, it was only possible to switch
to LC. I think that it was
Oriental Lumen that reversed this misguided, bigoted, and paternalistic rule.