Thanks for providing the websites. I just checked them. The initial connections is for sure being made as you've mentioned, but every GET request sent out past the initial request to get the content never complete. Additional requests are made to a CDN located in China for site resources, and to Analytics firms based out of China (similar to Google Analytics). None of these ever complete.
Running an MTR, I am seeing a huge amount of packet loss (>25%), with 500ms+ latency beyond Verizon Business in Los Angeles, through a peering gateway and onto China Telecom/Unicom's network. So what tifan mentioned about China Telecom having issues is very likely not to be that far off base.
It's hard for me to say if the problem is on Verizon's end, on a Chinese telecom provider's end, or a problem with an undersea cable that is creating such problems since traceroutes give limited info. I also don't have a looking glass server I know of which I can use in China to perform tracebacks. The reason why the AT&T network works fine, though, is due to the fact that they, like Verizon, are a Tier 1 network and likely connect up directly to the major backbone networks in the Asia Pacific region.
