What is the PIC equivalent to AVR's ICP?
The Microchip Advanced Part Selector lets you pick Microchip microcontrollers much in the way as the link for the AVR devices you linked to.

One of the criteria you can choose is "Input Capture".

There is no Search button; the results are updated dynamically as you change the criteria.

Note that there are several PIC families -- PIC10, 12, 16, 18 (all 8 bit), 24 (16 bit), 32 (32 bit), dsPIC30/33 (16-bit with DSP).