no, it isn't a more apt comparison. Antiqua and Fraktur look much more different from each other than most Chinese and Japanese characters are from eachother.
Here are two screenshots in Japanese and Chinese, taken from the http://www.yomiuri.co.jp/ for one, and http://www.cntv.cn/ for the other. Neither media outlet can be accused of being cultural sellouts misrepresenting the written tradition of their countries.
These are the same characters, and unifying them is the only sane thing to do. The same is true for most characters. There are also some characters which are clearly distinct in both scripts, and unicode treats them as different. Some are grey-zone, and there is room for reasonable disagreement.
But as a whole, the case of unification of Chinese and Japanese is stronger than for Antiqua and Fraktur.
Your screenshots are showing the exact same glyphs because you don't have the "宋体" font installed that's specified by the Chinese web page (it's a script font so you'd notice instantly it's different), so your browser picked a Japanese font to render it instead.
The only reason they look the same in your screenshots is due to Han Unification. Your reasoning is "they're unified in Unicode which is proof they should be unified in Unicode".
The fallback font used on my computer isn't the most appropriate one, but Japanese also uses Song/Ming fonts, and this is much more similar to the difference between a serif and a sans serif font than between different characters.
Here are two screenshots in Japanese and Chinese, taken from the http://www.yomiuri.co.jp/ for one, and http://www.cntv.cn/ for the other. Neither media outlet can be accused of being cultural sellouts misrepresenting the written tradition of their countries.
Japanese: https://www.dropbox.com/s/lpb3dk26ftds6oh/Screenshot%202015-... Chinese: https://www.dropbox.com/s/dcwv33ho0juracg/Screenshot%202015-...
These are the same characters, and unifying them is the only sane thing to do. The same is true for most characters. There are also some characters which are clearly distinct in both scripts, and unicode treats them as different. Some are grey-zone, and there is room for reasonable disagreement.
But as a whole, the case of unification of Chinese and Japanese is stronger than for Antiqua and Fraktur.