The .32 special was born in 1895 as a smokeless powder round that once fired could be loaded with blackpowder. The 30-30 came out a little earlier, but it's narrower bore and quicker twist fouled so badly that it's accuracy became eliminated in the first few rounds (when loaded with blackpowder that is). The larger bore of the .32 and the slower twist of 1 in 16 worked way better as a blackpowder round for repated firings. The .32 was more appealing to the man that had a lot of blackpowder. However, once the .32 bore is pitted, rusted or worn it's accuracy is horrible. Whereas the 30-30 can still deliver decent accuracy after it becomes rusted, pitted or worn.
There is virtually NO difference in power between the 2.
All information above "borrowed" from "Catridges of the World" By Frank Barnes