Aside from the redesign to the Menu button, the new Apple TV Siri Remote appears to be identical to the previous-generation model. At $59, the remote is $20 cheaper than the previous-generation Siri Remote.
Ahead of the launch of the new Apple TV, there was code found in leaked golden master software that suggested the new remote would feature new haptic feedback capabilities, but there's no mention of haptic feedback functionality in the description of the device.
The revamped Remote continues to ship with a Lightning to USB cable, and it is available with both the new 4K Apple TV and the existing fourth-generation Apple TV.
Apple is pricing the 4K Apple TV starting at $179 for a 32GB model. The fourth-generation Apple TV is available for $149.
Update: Apple notes in its overview on developing apps for the Apple TV 4K that the new Siri Remote is able to provide apps with data on attitude and rotation rate, in addition to the acceleration and gravity data generated by the original version.