I've got a 1917 from each maker, and I've owned an 03A3 in the past. No doubt I would take the '17 if I had to fight with a U.S. issue bolt rifle. Better sights and higher capacity do it for me.
Nothing inherently wrong with Eddystone's, they were the most prolific manufacturer of 1917s so they suffer from being more common. Winchester jumped the gun, and began building 1917's in .30-06 a month or two before the government had even finalized the specs for the model. This led to parts interchangability issues, and finally a blanket order for Winchester produced rifles to be held stateside for training and not go overseas with troops to the war zone.
This, along with Winchester's shenanigans producing the Garand during WWII, make me not a huge fan of theirs.
Frankly, I like my Remington 1917 the most, but that is only personal preference when comparing a trio of ninety-six year old rifles.