Today, China has 16 of the world's 50 busiest ports, including Shenzhen at #3 (all as measured by 2018 TEU volume). [4] However, this is less indicative of capacity than it is of current demand / throughput.
Both countries could benefit from building more deep-water ports. China currently has two Panamax ports, with a third on the way. Vietnam has none and is building its first. The U.S., by comparison, has 42 by my count. [5]
Separately, there's a great Wired documentary on Shenzhen: https://www.youtube.com/watch?v=SGJ5cZnoodY.
[1] https://www.latimes.com/world/la-fg-vietnam-trade-war-201907...
[2] www.scmp.com/economy/china-economy/article/3018403/chinese-manufacturers-returning-home-inefficient-vietnam
[3] https://www.wsj.com/articles/for-manufacturers-in-china-brea...
[4] http://www.worldshipping.org/about-the-industry/global-trade...