I'll be getting a 2013 if I do, which all I can find it that it achieved the highest ratings ever of any car across the board. The Ody I have now is almost just as safe with is 5/5 except in rollover which scored 4/5.
The ratings you're looking at are the NHTSA ratings, which is for a less stringent test.
IIHS has their own testing system which is more rigorous and more representative of real life accidents. It includes more scenarios of crashes and crashes at higher speeds.
In the IIHS tests, the older 2014 Odyssey tested performed better in crash tests than the "improved" late 2016 Model S which was retested following a redesign with new side airbags and other changes. Even with those changes, the Model S came up short. The crash test results before the changes (2012 - late 2016) has not been released. The Ody received the Top Pick rating and top scores across all tested scenarios. I expect the 2018 would only get better with standard collision warning/mitigation equipment.
A 2013 Model S would not have any Auto Emergency Braking or collision warning equipment, what Honda calls "Honda Sense".