The Eagle/Teebird is a classic one-two combo for Fairway Drivers. I have horrible BH arm speed, so (as you can see by my sig) I throw a lot of Fairway drivers. I ditched the Teebird last year because I much prefer the Vibrams. But I can't get rid of my Eagles. I have several 9x KC Pros and I just love to throw them. You can't really put them on a laser beam though (CORRECTION: I can't put them on a laser beam!) like I can the Vibrams. Eagles are line shapers, either mold. They also feel better in my hands.
I used Teebirds as my main driver for about three years, so I can tell you it is an awesome disc. With good snap and follow through that thing will be a frozen rope until right at the end when it has a nice, gentle fade. Also holds a good hyzer line, but not so good for hyzer flipping in my experience.
I would say technically the Eagle is a more versatile disc, but I would think you would find yourself, when throwing fairway drives, using the Teebird a bit more because of it's awesome straightness right out of the box. But I would say get both in DX Plastic and work with them to find how they work best for you...kind of a cop out answer but hopefully the info I provided above helps somewhat.