MAX7219 drives up to eight 5V, common cathode, 7-segment displays (plus decimal point), by multiplexing 8 anodes line and 8 cathode lines at 800 Hz rate.
TCIP6B595 is a high current/high voltage open drain output shift register. It can be used to sink current from common anode displays. If you add seperate anode switching control (discrete PNP transistor, PNP array such as UDN2981, or discrete P-channel MOSFET) you can use it to multiplex displays as well under arduino software control. Or you can just use more of them, 1 per digit, and skip the multiplexing.
(I've also used them in a multiplex situation to sink current Away from the LED anodes to keep LEDs off, while a NPN array was used for common cathode control (ULN2803). Allows for more current than a 74HC595 can supply- but also runs warmer as the current is either flowing into the display or into the TPiC6B595 all the time.)
The TCPI6B595 is useful for controlling things like 12V powered LED strip lights, which have their own built in current limit resistor. MAX7219 can't do that without additional hardware.