My experience, as someone who looks at both for every flight (104 segments so far this year), is that Flight Aware is not only more accurate, but that sometimes their departure estimates are hours apart, leaving those relying on UA's system in the lurch for trying to catch alternate flights by relying on unrealistic estimates. On one recent flight, UA's system said we would be delayed 2 hours but Flight Aware showed a 5 hour delay. Not trusting UA's estimate, I called the 1K line to see if I could find out what the situation was. They told me that they would have to bring over a replacement aircraft from the International Terminal at ORD (I was at my gate in Concourse C) and that this operation would take around 1.5 hours and, hopefully, result in a 2 hour delay. I decided that I didn't like the odds on that fix and had them re-book me. I ended-up routed through another hub but, in the end, arrived only around 30 minutes late to my destination and was on time for my business meeting. Out of curiosity, later that night I checked when the original flight departed and found that it ended-up leaving ORD over 6 hours late.

YMMV