For China...
1) A surviving Xin Dynasty (OTL lasted for around 20 years in the 1st Century AD) would have been awesome. Wang Mang basically tried to implement a economic system in China that was a mixture of state property (all farmland was to belong to the state), proto-central banking (controlling the price of inflation by buying/selling excess goods), and free enterprise (low-interest state lending to entrepreneurs and merchants). Less-admirably, the guy also thought it was a good idea to issue 28 types of currency in the Empire. Truly a man born way before his times.
2) A Northern Song Dynasty under Wang Anshi would have been interesting as well. Again, the guy tried to redefine the role of the Song state in China by making it responsible for regulating wages/prices, promoting economic business and creating a mini-welfare state of sorts.
3) Any surviving Warring State of the Warring States period, which could have provided an alternate counterpoint, cultural and otherwise, to the Qin Dynasty (though not likely, considering the pressures of the international environment at the time).
4) A successful Taiping Heavenly Kingdom would also be interesting, if only to see how the 'Christian' zealot leaders handle themselves in the midst of a largely Confucian populace.