You were very lucky to get 2-3 days; the overwhelming majority of iPhone users have to charge the phone every day. iOS 7 does not in itself use more power, but it added features that use power if you enable them.
You can check the actual usage by going to Settings/General/Usage. The "Standby" time is actually total time since the last full charge, and "Usage" is the total time the phone's CPU has not been idle. It obviously is not idle when you are using the phone, but there are a lot of apps, both built in and added from the App Store that can run in background, so this is also included in Usage. You can control what apps run in background by going to Settings/General/Background App Refresh. In addition, apps that can receive Notifications can run when a Notification is received. This includes any Push email accounts, plus apps like Facebook (probably the biggest user of Notifications), Words with Friends (and any multiplayer game), WhatsApp, Tumblr, snapchat, twitter, Instagram, etc. You can control this at Settings/Notification Center.
Apps that use Location Services can also run in background; you can control these at Settings/Privacy/Location Services.
You don't appear to have a sudden battery drain problem; that is usually associated with an app that is stuck in a tight loop. The symptom of that is "Usage" and "Standby" will be the same.