On its own, the Giant Eagle fills an interesting role. It is a cheap, high-speed flier with good melee attacks for the cost. While not as crushingly efficient as a Human Sellsword, this bird has lots of useful tricks that let it fill a couple of roles. It can serve as an inexpensive flanker that's more durable than a Deathjump Spider or a Mephit. It can chase after fodder and support pieces, using its Flight to go right over most blockers.
The Eagle's basic attack is just that; basic and simple. Flight should make it easy to line up charges, and if you set up a charge into a flanking position (usually later in a match, when the eagle is already behind enemy lines), it can be quite accurate. This is a perfectly acceptable basic attack, and you'll use it a lot.
The Flyby Attack can be used only twice, but that's fine; it's a two-use way to 'break the rules' of movement and attacking. The ability to move, attack, and use your remaining movement is more potent than it sounds. The most obvious use is to simply hit an opportune target along the way to where the Giant Eagle really wants to be, but there are other tricks. You could, for example, fly out of your victory area, hit an enemy, and return to the victory area to score points. You could use narrow hallways to cycle the Eagle in and out of the fight while your heavy hitters hold the front line; it's the ultimate skirmisher.
Power Dive, however, is a real gem. It's certainly the most fun part of the creature -- it's impossible to not make avian 'skree!' noises when declaring Power Dive. What's really important about it is that Power Dive is not an attack. That means it ignores Conceal (which affects only melee and ranged attacks) and Insubstantial (which affects only attacks). Because it is automatic damage, there is very little your opponent can do about it. Save it for those high-value, hard-to-hit targets or something with only 10 hp left that you really, really need to destroy this round. Synergies
While the Giant Eagle can work fine alone, it goes well with heavy hitters that benefit from flanking-based combat advantage, such as the Everfrost Ranger. A lot of hitters in Wilderness and Borderlands cause high damage but have low attack bonuses, and this bird helps with that. Amongst Champions, the obvious choices include the Eternal Blade and Hierophant of the Seventh Wind, though the Blade might be better off using her champion powers on more valuable creatures. 500 Point Play
While the Eagle retains some value as a cheap flanker or fodder hunter in a 500-point environment, it's hard to recommend Big Bird in this format. Its attack value and damage output are low, and it fails to fill the same niche it does in 200-point warbands. It's best use here is probably as a reasonably durable victory area grabber.