Just to pitch in from my point of view. My home airport is LIM. I used to fly Copa when MileagePlus was both Copa+United. When they separated the programs, I stuck with United because all my miles were here already. I've had my fair share of both Copa and United flights, and let me dig in a bit.
In the past, I used to do a LIM-PTY-XXX route, all Copa, or LIM-PTY Copa, PTY-IAH-XXX United. Now I do LIM-IAH-Wherever in the US with United. It's saved me time.
In the past, I've gotten free meals from Copa. Now, I still get free meals from United, because of the length of the LIM-IAH flight. When I arrive to the US, it's already time for breakfast, and I've already had a snack on the plane, so I just grab something small in the lounge. What I like about Copa is that they give you real cutlery to use, while in United it's all plastic cutlery. But I believe United's food is better (I love their marinara).
Copa has A LOT of daily flights from LIM to PTY (in 757s). However, PTY is an okay airport. Small-ish, a bit disorganized, and wifi is horrible. United, however, only has 855 from LIM to IAH (in 767s), and the occasional 1005 from LIM to EWR (in 757s). I think IAH is better, and has a huge variety of things to see around.
The only lounges in PTY are the Copa Club (pretty exclusive, never got to go inside) and one lounge landside). In IAH, there's several United Clubs, a KLM Crown Lounge and an Air France Club. Of course, it has more terminals, and that is to satisfy the number of people who use the airport.
Customer service in Copa (over the phone) is horrible. They don't treat you well, and if you ask for a complex itinerary they just want to get rid of you. They almost always know nothing. Believe it or not, UA's customer service is WAY better than Copa's. Agents always try to help out (even if they take long), and get to give you a hand.
As a non-status passenger, I really liked the fact that I could get free exit row seats in Copa. My native language is Spanish, so I've never had a problem there. But for United, I kept on flying on regular Y, because I knew at some point I would strike the free E+, and now I enjoy even better seats (17/18B on 763s <3). I must say, I have seen people in United being booted out of Exit Row seats because they didn't understand English, and they have to speak the crowdmember's language.
Flight attendants in Copa are always willing to help, with a big smile. I've had a couple times where they must've had a bad day, but in general they are very nice to you. In United, you can get mixed experiences. I've only struck one or two unhelpful FAs, but they were really bad experiences.
For baggage allowance, when you are flying out internationally, United does give you two free checked bags at 50lbs. No charges for the two checked bags. And I believe Copa only has international flights to/from the US, so it's very similar there.
Aaaand I think that's all I can say. It's 2am here and tried to spot most things. I do prefer United over Copa, yes. Just a matter of personal preference. However, I wouldn't avoid a Copa flight. If it's an option to fly instead of United, I do consider it. I'm just thinking on my lifetime miles and stats, and... welp, you get it. I like Copa, I like United, I prefer United.
PS: Sorry for the wall of text!