Quoting Aurantiaco (thread starter), "Which would be better to fly?"
Aurantiaco, when comparing American and Southwest, I don't think there is a "better" airline between the two of them. Personally, I think they are equal in terms of safety, reliability, punctuality, and professionalism of the pilots. In terms of frequency, I think both American and Southwest generally operate four flights per day between DFW/DAL and BWI.
Now this is just personal opinion--to which I am entitled--so please do not label me as an "American hater" or a "Southwest lover" and flame me for an opinion but this is based on personal experience with approximately equal number of flights on Southwest and American and when I fly American, I always fly in coach/economy (so as to provide a comparable experience with Southwest). And also keep in mind, these are just "snapshots," someone else's experience on either carrier may be completely different than mine on any given flight.
The question I would ask in this case is "How do you prefer to be treated?"
Every company has a defined corporate culture that begins with top leadership and permeates throughout the entire work force and this is where I see the difference between American and Southwest. American seems to have a "global domination" mentality (which did not start with Doug Parker, by the way, it goes way back to the Crandall years or even earlier) while Southwest's corporate culture is more "local business" and "community partner."
When I travel American, I feel like the employees are generally rude, abrupt, disrespectful, and disinterested in the passenger. I always get the feeling as though the employees are trying to convey to me that if I don't like the way I'm treated, since they are the largest airline in the world, they do not care if they lose my business since there are many other people who will take my place and travel with them. On the other hand, when I travel on Southwest, I feel like the employees are genuinely friendly, kind, respectful, and enjoy their work. They seem to convey to me that they value the business of each and every customer and would like them to return.
As others above have stated, there are other difference for you to consider. Assigned seating vs. open seating; fees for checked luggage vs. bags fly free, etc.
On Southwest, I never pay the additional charge for early check-in (or getting an A group). I just check in 24 hours in advance of the flight and generally end up with a mid-B number and I have found I am still able to get my favorite seat (a window seat) somewhere near the back, which is fine with me. Also, with no checked luggage fees on Southwest, I find fewer people tend to carry enormous suitcases aboard the aircraft and boarding seems to go faster and smoother than on American. On American, with assigned seating, I also do not pay for ugraded seating and generally end up with a middle seat near the back.
One last thing, the method by which the flight attendants serve beverages is a little different. On American, using beverage carts--the flight attendants generally make one pass through the cabin. At Southwest (on comparable length flights) I have found that after the flight attendants take your order and deliver the beverages, they usually come back to see if you would like an additional beverage. Of course, this is a fairly minor difference.
That's my opinion. Just to be clear, I have many friends who work both for Southwest and American, and I actually interviewed to work at both Southwest and American (although I ended up deciding to work for another airline other than Southwest or American) and I think they are both terrific companies. Despite what you may think, I still fly American frequently when their departure/arrival times are more convenient than Southwest or when I travel to a destination not served by Southwest.
You will have a great trip regardless of which airline you choose, but in answer to your question, if I were traveling between the Dallas area (DFW or DAL) and Baltimore, I would choose Southwest. For me, Southwest would be a more enjoyable travel experience. Perhaps you should fly American between DFW and BWI one time; the next time you go visit family choose Southwest DAL - BWI.