a T-Bill future is an discounted rate thingie
a Eurodollar future is a Add-on rate.
1-r*T/100
vs.
1/(1+r*T/100)
with the two - you can never find a proper rate T - that meets both equations properly and makes an arbitrage condition possible.
however, the eurodollar future can be still used for hedging, so it is a useful thing to have around.