I agree, contact your landlord. Although the other tenant may rent from someone else, your landlord should be able to help you.
It reminds me of a commercial I saw recently. It showed a successful barber shop. Then a scene where across the street a $6 barber shop opens. It then goes to a scene with the old shop covered in signs that say "We fix $6 haircuts". The final scene is of the new place going out of business.
If all else fails, put someone out there right next to this guy with a bigger sign .... plus someone at the front of his entrance. But, I'd avoid getting into dueling signs. Work it out with your landlord, I would think they would be interested in keeping your business going strong.
Keep us posted how things go with this. Welcome aboard