SqueeGee
Normally, I would suggest that if you're that worried about your competition, you really ought to focus your energy on differentiating your products/services. And I'm not sure that's bad advice in this case either. However, you shared some specifics that seemed worthy of comment.
In the case of the agency that just started outsourcing (and in the case all new clients, really): I would suggest seizing the opportunity to ask how they found you, and what made them decide to give you the business. What other suppliers did the agency consider, and why did they rule them out? You might just glean some valuable competitive intelligence - which will either set your mind at ease, or reinforce your reasons for concern. Either way, you'll be able to act -- on fact, rather than on conjecture and opinion.
I would strongly consider having a similar conversation with some of your biggest and best clients. Why do they keep coming back to you? On a scale of 1-10, how likely would they be to recommend you to a friend or colleague? If there was one thing you could improve about their experience with buying from your company, what would it be? What other sign companies did they use in the past? How likely would they be to recommend those companies on the same scale?
In the case of this copycat competitor: The real question is how, specifically, is what you're offering at your prices different from what he is offering at his prices? What are your competitive strengths and weaknesses compared to this guy? What value do/can you offer customers that would be difficult or impossible for him to duplicate? Develop your strategy accordingly.
If you want to have some fun: create a list of your worst customers...PITAs, slow payers, nickle-and-dimers, whatever... and whenever any of them they call next: apologize, tell them you are really up to your eyeballs in work, and send them to your pal. He'll no doubt take the work, and you'll bog him down with all the problem customers.
