It's not a matter of meaning, it's a matter of context.
Unarguably, Bob is an excellent teacher.
This is an assertion about Bob's teaching excellence. The speaker expects no one would either question or dispute how well Bob can teach.
Arguably, Bob is an excellent teacher.
Once again, Bob's teaching ability is being affirmed. However, this sentence seems like it's a little more likely to be followed by a but or a however:
Arguably, Bob is an excellent teacher. However, he doesn't get along with his coworkers very well.
Another difference is that unarguably doesn't work well when talking about greatness that cannot be measure objectively. For example, I think it's okay to say:
Arguably, Bobby Orr was the greatest hockey player ever.
because some believe that is true. However, it would be foolish to assert:
Unarguably, Bobby Orr was the greatest hockey player ever.
because many people would bestow that honor upon Wayne Gretzky instead.
In other words, avoid using unarguably to describe matters of opinion, but reserve it for matters of undisputed fact:
Unarguably, the world's population has increased since 1900.