Only COA flies the 757-300 so that's one way to tell the difference. Also, the tail number could be a give-a-way for the 200s. Typical United tails are N###UA while COA are N#####. Obviously doesn't always hold true but could give you a bit of an idea. I know COA's website used to (may still) would allow you to see all details (engines, configurations, etc) of an aircraft assigned to your flight.
Did DAL sell off the B753s they inherited when they bought NWA? I know NWA flew them.
Anyway, the easiest way I've been able to tell the 752s apart from the 753s is the forward section of the fuselage. On the -300, That section is stretched a bit more between the main cabin door and the next emergency door, as compared to the -200. After that, they pretty much are the same.
The other way I could tell them apart (now obsolete), was that when the FAA had the 250,000lb MTOW limit between large and heavy aircraft, the B753 was always a Heavy jet. now that it's raised, you won't hear that. But mainly for me, I can tell by the forward section of the fuselage.
BL.