Eventually, I'll add a Q and A detailing why I -- like every foreigner I know -- believe that Taiwan adopting tongyong pinyin for Mandarin is a terrible idea, and why using an unmodified hanyu pinyin is by far the best choice.
But for now, here are comparison charts, listing possible syllables. Because a u with an umlaut (two dots above it) doesn't show up properly in all browsers, and because even if it did some people wouldn't be able to find it through searches, I've followed the convention of rendering it with a capital U.
Note that the version of tongyong pinyin given here is not the same as the one being used on some street signs in Taipei. Why? Tongyong pinyin seems to have changed several times since the signs went up. The version given by the GIO is also out of date.
Comparisons:
ZHUYIN, hanyu pinyin, tongyong pinyin
zhuyin, HANYU PINYIN, tongyong pinyin
zhuyin, hanyu pinyin, TONGYONG PINYIN