There's one critical difference, which is that only chartered banks within the Federal Reserve system can take advantage of the federal funds rate, whereas anyone (including individuals) can buy T-bills.
The Fed, for various reasons, implicitly disallow this type of narrow bank. Several people have tried but the Fed always denied their application to join the system.
Coincidentally, just two days ago I commented on the distinction to someone suggesting this kind of service: https://news.ycombinator.com/item?id=35790913