They are both phenomenal guitars. Personal preference in feel and desired sound should determine which you get. Fenders generally give a brighter, brassier sound, while Gibsons are known for giving a warm, rich tone. If you're not an experienced guitarist, you probably won't be able to hear too much of a difference though.
The other major difference is the neck angle. On a Gibson, the neck is bent back towards the player slightly, which is why the bridge is raised. Fenders, however, are totally flat in terms of neck angle. Personally I prefer the feel of a Gibson, even though I learned electric on a stratocaster.
Go to guitar center and play each one for a bit. Take the one that feels best and most natural to you.