Our home base is Tokyo Immigration at Shinagawa. We basically visit there every Wednesday.
But exceptionally, I visit branch offices upon to client’s request.
Some believes some branch is faster and easier to get a visa. But generally, it is just a rumor. Of course if you do simple extension, branches that are not so much busy as Tokyo Immigration would take shorter time for procedure. But if you do extension with difficult issue, changing visa status, COE application, PR application, your case would be transferred to main office and is examined there. So no difference at all.
So I advise/ request our clients to apply at Shinagawa. However, some wants us to apply at branch. Of course, our office is trying to follow the clients’s request, if it is reasonable and if we could manage to make it.