Yes, if there is some specialty that the competitor is very proficient in, and you are "moderate" in that aspect, you are already swapped with jobs and to say if this is something that you need now, I would recommend that you try and then give the name.  Now, of course, if we are not busy and can handle the job, then We would go ahead.  But, sometimes, you have to think, that you might loose if you try to push another job in where you are already tied up to many projects.

Think about the reputation that might come with word of mouth.