They are both very nice bows for a strafer. Note that the Eagle gets a level dependent bonus to damage and AR while the Goldstrike does not. So your characters level is important and the level you are aiming to build up to.
Also Goldstrike gets quite a wide range of variable mods. These are %ED 200 - 250 , Bonus AR 100% - 150%, and %ED to Demons and Undead both 100% - 200%. So the difference between a near perfect Goldstrike and a poor one is huge, so you need to give the statistics of the one you're considering.