CAN (or one of its more modern variants) are historically more common in automotive. However with 2-wire Ethernet connections becoming more commonplace I do think you're right that more and more cars will be moving to ethernet fieldbus.
EtherNet/IP is not as robust for many applications as its competitors (PROFINET, EtherCAT) since it is not fully deterministic. EtherCAT is my personal favorite.
Please no EIP, its utter crap and designed by an OOP huffing committee. The only serious protocol is EtherCAT with honorable mentions for Sercos 3 and Ethernet Powerlink (CANopen over Ethernet).
Of all the (current) industrial protocols they could have picked, Ethernet/IP would be the worst.
Its only advantage is that it can coexist with other TCP traffic and run over standard switches, but that just results in unreliable fieldbus performance.