Protecting BJT base-emitter junction from breakdown voltage
As you draw it, there's no difference assuming you've either not connected the BJT's collector or shorted it to the base.

In a real circuit there might be a difference as then the collector might come into play.

So depending on the complete circuit it could make a difference if the extra diode is in series with the base or the emitter.

In most circuits the low base-emitter breakdown voltage is not an issue. In some circuits it can be though.