Alltelll is competing with all other cell phone providers, but particularly with Verizon. I know this from the commercial that Alltel is currently running, featuring a family in an RV discussing cell phone plans with representatives of all other wireless networks, prominent among which is the Verizon "rep" with the company name inscribed on his red shirt (red also being one of Verizon's colors).  Quizno's "meaty" sub is far meatier apparently than a comparable meat sub at Subway. They told me so.

We see this side by side comparison frequently in political ads but not as often in product/service ads. Why? Because it is risky. First, there is the risk of libel. If you say anything really bad about the rival, especially something unfounded, then you can be sued. Second, you place yourself in direct competition with something particular, practically begging for people to compare and contrast. As an advertiser, you have to be supremely confident in your product/service to attempt this. Remember the cola wars? Pepsi and Coke challenged people to taste tests!

Another issue with mentioning your competition by name is that you are revealing to the competition just who/what you consider your biggest competitor.  For Quizno's, it is Subway. Subway knows this. A while back, Subway started offering "toasted" sandwiches. Quizno's is known for their warm offerings.

I understand why you would challenge your competition. You want to prove superiority. However, this strategy can backfire in some cases.