the avr-libc offers functions to access the AVR internal devices only. The AVRlib was much more general in my opinion (external flash memory access, LCD, Servo, network,...). IMHO, Webbot library is a replacement for AVRlib.
I see avr-libc as foundation for higher level lib. You certainly used it already if you use AVR GNU toolchain (avr-gcc, avr-ld,...) or WinAVR.