I'm a UA flyer on the fence about leaving so I'll chime in from my perspective.
The things keeping me with UA are the following (and in order or importance to me)
1. Same Day Change Policy is the best in the business for gold and up. You can change for free for flights 24 hours before your flight or within 24 hours of the time you're requesting it if you're inside the 24 hour window. So say you have a 9 a.m. flight on 4/30. On 4/29 at 9 a.m. you can make a change to ay flight leaving before your 9 a.m flight. At 9 p.m. on 4/29 you can change it to any flight up until 9 p.m. on 4/30. It does not have to be the same day of the flight which is what makes me want to stick around. I've cut short and extended trips so many times thanks to this. I've also managed so SDC on to more desirable routings or lesser connection times with no fee whatsoever. Only caveat is the fare class you booked has to be open on the flight you want to change to. UA typically opens up all fare buckets near the flight time so I rarely have an issue. Since you can have unlimited changes, you can keep changing up until you get what you want. IMO this is be best benefit of the airline program period.
2. Star Alliance Network is wonderful.
3. No YQ on Award Tickets. When you try to redeem your first J award on BA you'll understand the value of this.
4. Miles for me have been easier to use.
5. Since I do travel to Canada, UA is a better fit for me with the AC partnership.
6. Fear of the unknown. Doug Parker is the devil I don't know and Jeff Smisek is the devil I do. I don't like the one I know, but I'm afraid that the US mentality will take over AA the same way the CO mentality has taken over UA. What I do know about US is miles are very hard to redeem, especially at the low saver rate. They have no one way trips (which I value). We've already seen one major devaluation and elimination of some excellent benefits of the AA program (most notably award stopovers in the international gateway). If he goes all Smisek on AA, then we really won't be left with much of a choice. I have 150K US miles thanks to Grand Slam, and I have had a hard time using them every time I've checked. That scares me.
Now those benefits do not come without costs:
1. Upgrades are becoming harder and harder.
2. Service is very inconsistent.
3. The CO mentality of management is not very customer friendly.
I did try AA as an EXP the first year they did the match, and I still found myself happier on UA because even EXP has to pay $75 for a same day flight change unless you want to stand by (which is free). But if you stand by, you pretty much lose any chance of an upgrade because upgrades tend to process before stand by. And you must do it on the day of your scheduled travel (not day before or day after like UA allows).
One thing that appeals to me about AA is the Choice Plus offerings. I don't exacly get free same day changes, but if I pay the initial fee, then I can change the flight with no change fee and will pay only additional fare if there is any. I'm not sure how AA is about opening up fare buckets close end though. Perhaps someone can elaborate.
Every year I find myself on the fence about which program would be best for me. I've considered doing US Trial Preferred to get status with OW to try things out. Making CP would not be too difficult in the 90 day challenge, and if I start it at the right time, I will keep it all next year as well.