Team win has released latest version of TWRP for Galaxy Note 3. You can download Note 3 TWRP from the link given at the bottom of this page. The TWRP is the most popular custom recovery and many prefer it over CWM as it allows users to interact via touchscreen.
In this Note 3 TWRP you can use onscreen keyboard to input data. In other words it is a must have if you are into flashing custom ROMs. Samsung is really sluggish in pushing firmware update.
This Note 3 TWRP also allows you to backup and restore partitions. Also after some time you may get bored of the user interface but don’t fret as you will be able to easily skin with bucketful of TWRP themes available online.
Samsung Galaxy Note 3 Canada (hltecan)
Samsung Galaxy Note 3 International Exynos (ha3g)
Samsung Galaxy Note 3 International Qualcomm (hlte)
Samsung Galaxy Note 3 Sprint (hltespr)
Samsung Galaxy Note 3 T-Mobile (hltetmo)
Samsung Galaxy Note 3 US Cellular (hlteusc)
Samsung Galaxy Note 3 Verizon (hltevzw)