Otabek

the question asks to choose between eurodollar contract and tbill futures. so hence euro dollar is better choice.

from practical stand point, it is not "A PERFECT HEDGE" like you indicated. There are other products out there that you can use to hedge paying/recving cashflow. However, these might not be feasible since the transaction cost/operational risk might outweight the benefit.

eurodollar contracts happens to be one of the most liquid libor based instrument out there. you can easily buy/sell to express your views on the front part of the libor curve. hence, people choose eurodollar contracts over other libor based instruments. this liquidity disappears if you go further out the curve, say, more than 5 yr (gold pack). in that case, most will use swap.

good example would be swap spd. when a trader wants to take exposure in swap spd and he wants to express his view that yield on 2yr note will decrease vs 2yr libor rate (swap spread widener). he will most likely be buying 2yr tsy note (spot settling) vs selling eurodollar contracts (fwd settling). the reason for his choice is to mitigate the transaction cost of his trade and take advantage of liquidity.