I'm assuming you're looking at the Vita line? Here's a comparison between them Specialized Bicycle Components
The Comp jumps to a 2x10 (20 speed SRAM) drivetrain instead of the 3x9 (27 speed Shimano). It's more road oriented, and is a higher end drivetrain than what comes on the Elite. The Comp also has some other upgrades, bar ends, wheels, brakes, crank, etc. If they'll give it to you for the same price as an Elite, then it's a good deal. I would do it as long as you didn't mind the color difference. Yeah it's a really good deal and more bike for the money, just make sure you're not going to think "I wish I had that emerald color instead" every time you look at it. If that's going to be the case, then maybe you could convince them to give you the Elite for an equivalent discount or close? If the color doesn't bother you much I would definitely get the Comp then.