When calculating the probability of a certain target rate specified by the Fed at an FOMC release, I’ve generally read that it is typical to use Fed Funds Futures as proxies. I can find data on this on the CME’s website. Bloomberg also has functionality to perform this calculation, but they use OIS’s to estimate the probability. When comparing the two methods for a given FOMC meeting date, they give fairly similar, but not super close answers, say in the range of 5%-10% max difference. What is the theoretical basis of using OIS’s is, as opposed to Fed Funds Futures? Is one more correct? Any source material is appreciated.
I think you have a little misunderstanding. OIS just means the rate for fed funds. Usually people are referring to "FEDL01 Index" on Bloomberg. That's the VWAP of trades for the previous day in Fed Funds with participants lending to each-other. That's all in the past. That tells you nothing about the future.
The Fed Funds futures settle to the average over the reference month for FEDL01. That's forward looking. If you are looking at what the current market thinks Fed Funds will be at point X in time you have to navigate the Fed Funds futures.
I'll show you here the Fed Funds futures market right now: