The Xperia Z1 comes with a 3,000mAh capacity battery, which is similar to the HTC One and Samsung Galaxy S4. Sony also gives you access to its power management tools that include Stamina mode to disable data when the screen is off and a low battery mode to conserve power when you have reached critical battery life levels.
On full charge and in general use playing games, browsing the web, and using Twitter and Facebook, the battery can last through a day. Further, you can actually get a around a day and a half of proper use, if you are not using it excessively. Connectivity-wise, the Xperia Z1 will feature the normal connectivity modes including Wi-Fi, 2G, 3G and Bluetooth.
On the other hand, the Galaxy Note 3 comes with a 3,200mAh battery, in order to compensate for the larger, higher-resolution screen. There is a Power Saving mode that'll help to get the maximum running time out of your mobile. In terms of connectivity, you get NFC, 4G, Bluetooth 4.0, and IR transmitter and MHL.
Samsung also offers a few apps that try to make better use of the lesser-used connections. Samsung Link is a Wi-Fi-based connectivity app that lets you speak to other Samsung Link devices. Group Play uses NFC to let you share music with other Samsung phones. There's also a Wi-Fi Direct sharing option within the Gallery – Wi-Fi Direct uses a Wi-Fi signal, but doesn't require internet connectivity.
