Are you buying on-contract or off?
They are actually pretty different device because of some hardware difference (wireless charging) and software tweaks, but I feel like the Moto X is better for casual users. Nexus 5 I feel like is a more multimedia device. Personal take, of course.
In terms of overall speed and performance, both are excellent, though I would say the Nexus 5 camera is easier to use than the Moto X's, if a bit slower to focus. Battery life will depend on your coverage/app usage, but I would say the Moto X has a slight advantage.
Sorry, probably wasn't any help here haha. I just bought both =x
Grab a Nexus 5 off contract, and then if you don't like it, you'll have an upgrade available (hopefully). Either one would be fine for your uses, but the main differences are physical size and Active Notifications. I prefer the Moto X, but if you aren't sure, then buying a Nexus 5 off contract first will allow you to switch devices since you won't be locked in. Of course, if you are looking at the Moto X because of the sale today, then I would go for the Moto X.